Speaking to Jorge Valdano in an interview for Movistar Plus's Universo Valdano programme, due to air in full on Friday, the Barcelona forward was more emphatic than in previous public comments on the subject.
"Who would I give it to? To the best player in the world. Who will they give it to? That's a long conversation... I honestly believe the best in the world are two of us, and this year I think I deserve it for what I've won," Yamal said. "For me, Mbappe and I are the two best in the world. That's clear to me, and everyone who watches the matches knows it."
It marks a shift in tone from the Spain international, who had previously played down his chances at a press conference before Barcelona's Champions League opener against Feyenoord.
"It doesn't depend on me, it depends on you. The work with Barca and the national team has been incredible. I have a chance, I had a great year. But we'll see. I don't think I need to campaign. Everyone can think what they want. I'm proud of what I've done and I can't ask for more. It's your job, I won't beg for anything," Yamal had said at the time.
Members of Barcelona's hierarchy have also thrown their support behind Yamal's candidacy in recent days. Head coach Hansi Flick described him as "a special player" who "deserves it," while club vice-president Rafa Yuste was even more direct, saying: "I hope justice is done and they give the Ballon d'Or to Lamine."
Real Madrid forward Mbappe was the first of the two rivals to stake his claim, telling reporters ahead of a Champions League match against Inter Milan that people naturally associate him with the award after a historic World Cup campaign. He later doubled down in an interview with France Football.
"Being the all-time top scorer in World Cup history and overtaking all the great legends in the sport's most important tournament is something that burns the retina, a global event," Mbappe said. "Who do I vote for? Myself."
Yamal also revealed the standards he holds himself to, admitting he was not satisfied with his own performances even after winning the World Cup with Spain.
"After winning the World Cup I wasn't happy. I did a lot of things people didn't see. For a coach it's incredible to have a player who drags three opponents with him, but I wasn't happy for myself, because another player with my output would have had a great World Cup, but for me, I could have done more," Yamal said. "I did help the team, but I really want the next one to come around."
Despite the rivalry appearing to be a two-horse race, this year's award is regarded as one of the most open in recent memory, with candidates including World Cup Golden Ball winner Rodri, treble winner Fabian Ruiz, Golden Boot winner Harry Kane and Khvicha Kvaratskhelia also in contention. The Ballon d'Or ceremony takes place on 26 October.