The next door he knocked on opened only reluctantly. Alexander Zuev, the coach at the mini-football school Vostok, refused to watch the boy at first, then agreed to a single session, and Sport-Express reports that Batrakov's parents heard him say afterwards: "I need him."
Zuev later recalled that the five-year-old read the pitch as though he were looking down on it from a helicopter.
Height was the only objection, and it has never fully gone away. At 173cm, Batrakov spent years in Lokomotiv Moscow's academy while a coaching council regularly debated whether he was physically developed enough to stay. Andrey Nagibin and Andrey Altukhov argued each time that the football quality was there and the body needed time.
Time has proved them right. On October 21 Batrakov rose to head home on 44 minutes at Lille, levelling the Champions League game at 2-2 on the way to a 4-2 win. Galatasaray manager Okan Buruk said the goal owed much to Roland Sallai's work on the move "and the fact that Batrakov was in the right place", before talking about the player himself.
"Batrakov is hungry for the game, hungry for success. He is eager to play in the Champions League," Buruk said. "He is a passionate player, and in football that is one of the most important things." Speaking after the match, the manager added: "He tries to give everything. He works very well."
Buruk also expects the improvement to continue.
"I think the more he plays, the better he will become," he said.
That goal followed another a week earlier. In Istanbul this month, Batrakov opened the scoring against Barcelona in a game Galatasaray went on to lose 1-4, the first Champions League goal of his career and his first for the club. He became the ninth Russian to score against Barcelona in the competition, and the first since Andrey Arshavin in 2011.
His reaction, given to Sport-Express after the match, was disbelief.
"Honestly, I don't realise yet what has happened," he said. "It all happened so fast that I'd like to live it again."
He had spent the evening pressing the opposition midfield: "I got into the rhythm of winning the ball straight away, I ran from Rodri to Pedri."
He did not let the names bother him.
"If I'd thought too much, I would have burned out and not scored," Batrakov said. "I'm a maximalist, like everyone in our team. I only thought about winning."
Barcelona manager Hansi Flick had been asked about him the day before, at a press conference reported by Euro-Football.
"If you are young and talented, you always dream of something great," Flick said. "For example, of playing for Barcelona, as Batrakov dreams of, if you've said it correctly."
Batrakov's response afterwards was typically measured: "Flick said he's following me? That's a big claim. He watched one game. I hope this is only the beginning."
At home, the reaction has been warm and, from one prominent voice, direct. Alexander Alaev, president of the Russian Premier League, said this week that he was pleased Batrakov had not stopped "at one goal in the Champions League and immediately scored a second", and said he was sure the midfielder has a "big future".
Lokomotiv manager Mikhail Galaktionov was warmer still. Asked by Sovsport whether Batrakov should aim for the Ballon d'Or, he replied: "Setting that goal is a must, 100 per cent, because Alexey is one of the most talented young players in Europe."
He added: "Our boy is simply clever and wonderful!"
Russia head coach Valery Karpin has been more guarded. In September he said: "The move [to Galatasaray] is okay, a good one. But the main thing is to play, not to move."
A month later, after the Lille game, he said: "Of course, nothing supernatural has happened. The fact that a new footballer from Russia after Aleksandr Golovin stands out at this level is important too."
Batrakov says that when he reported to national-team camp, Karpin simply asked him: "How are you doing, Turk?"
Not everyone in Turkey is convinced. Sergen Yalçın, the former Beşiktaş manager, said earlier this week on the YouTube channel Kafa Sports, "Batrakov is not a bad footballer. I don't want my words to be misunderstood. He is perfectly capable of playing in the number eight position. But he isn't the player Galatasaray need in order to win matches, and he never will be."
The player's own account of the move has been uncompromising. Asked in a Sport-Express interview in October how he reacted to the criticism in Russia, Batrakov replied: "Honestly, it makes no difference to me at all. It's my decision, my football path. The main thing is that I'm happy."
He was equally frank about what he left behind.
"In the current situation, unfortunately, the championship isn't developing: there are no star players you can learn from, there are no European competitions."
Nagibin, the youth coach who brought him into Lokomotiv's academy, had seen it coming.
"If there really is an option with Galatasaray, and the clubs manage to agree, he has to go," he said in August. "I read that Alexey himself is already asking the management to let him go. I think there is no point in keeping a player whose mind is already at another club."
Batrakov joined from Lokomotiv for a reported €25 million in the summer, after 15 years at the club, and is the first Russian in Galatasaray's history. His wife, the former Russia international Irina Podshibyakina, moved with him.
"I love, respect and value the fact that she left everything in Moscow and came with me," he said.
His Lokomotiv numbers explain the fee: 14 league goals in 2024-25, third in the scoring charts, a hat-trick against Spartak Moscow, and Young Player of the Season in the Russian Premier League in both of his last two campaigns. He scored on his Russia debut, against Brunei in November 2024.
On the pitch he is an attacking midfielder who wins games with timing rather than power. His first touch is quick and clean, he rarely beats a man on the dribble, and his best work comes from finding the pocket of space a split second before the defence does, a Raumdeuter in the mould of Thomas Müller more than a traditional number 10. That reading of the game explains how a 173cm player keeps scoring headers.
Turkey's stadiums have taken some adjusting to.
"A person who hasn't been to matches in Turkey won't understand what is going on in the stadiums," he said. On his Champions League debut, the anthem nearly undid him: "I looked away from my parents so as not to cry."
Nine appearances in, he has two goals and two assists, which is the kind of answer Karpin was asking for. Whether it ends in the Barcelona move he once dreamed of is a question for later. For now, Batrakov's own measure is simpler.
"I catch myself thinking that I'm happy right now," he said. "That's the most important thing."