The 16-year-old finished the tournament as one of Brazil's standout players, contributing two goals and two assists in six matches as Brazil finished third.
Barcelona have also been heavily linked and are believed to have made a strong impression on the player's thinking.
However, ESPN Brazil reports "ongoing daily contact" between City and people close to Conceição, with a source close to the player summarising the situation simply: "All the big clubs in Europe want him."
Chelsea, Arsenal, Liverpool, Newcastle United and Paris Saint-Germain are also involved in discussions.
Palmeiras are in no rush to sell. Eduardo cannot move to Europe until December 2027, and the club are holding out for a fee closer to €50 million — above the €40 million that has been floated in recent weeks.