If the bid is accepted, Felix would become the third-most expensive player of all time behind Neymar and Kylian Mbappe, who joined Paris Saint-Germain in 2017 for €222 million and €180 million, respectively.
"Atletico Madrid have presented a proposal for the definitive acquisition of ... the player Joao Felix Sequeira for an amount of €126,000,000, which is being analyzed," Benfica said in a statement, according to Agence France-Presse.
Felix already agreed to a five-year contract with Diego Simeone's side, according to multiple reports.
He'd replace Antoine Griezmann in Atletico's new-look attack. Griezmann, who announced his departure after five years with Los Colchoneros, is likely to join one of Barcelona or PSG in the summer transfer window.
Felix, who can play on either flank, is coming off a breakout campaign in which he scored 20 goals in 43 matches across all competitions.