Newcastle were the first to submit a formal bid, reportedly around €25 million, which was turned down. Arsenal made early contact with the player's representatives, and Chelsea have since entered the picture — following the template they used to sign Estêvão and Endrick before them.
Palmeiras, however, are not selling.
The Brazilian club have made their position clear: no departure before the player is ready, and any future deal will require a fee in the region of €60 million or above. His contract runs until 2029 and a €100 million release clause protects him further.
For his part, Conceição seems entirely unbothered by the noise surrounding him.
"The pressure is something natural for those who play for Palmeiras," he told Spanish outlet AS. "We are used to dealing with it from a young age."
He admits he deliberately avoids the headlines.
"I do not usually read the news about me. My daily goal is to be in the best possible condition to show my value on the pitch. My agent knows that I do not even like to keep up with what happens outside football."
His family keep him grounded. His influences are close to home.
"Endrick and Estêvão are the biggest inspiration for all of us who are chasing our dream. I have followed their paths and I hope one day to do what they did for Palmeiras."
The connection is personal as well as professional — one of his agents is Douglas Souza, Endrick's father.
In terms of style, Conceição describes himself as a direct, right-footed winger who thrives in one-on-one situations. He cites Estêvão and Lamine Yamal as comparable profiles. He has scored five goals and provided three assists in 13 youth appearances this season.
His ambitions for now are modest and grounded.
"My dream is to have the opportunity to debut for Palmeiras' first team and make a difference on the pitch, like others have done in recent seasons."
Palmeiras are in no rush to grant Europe that wish.