The offer is above the 19-year-old's 120m euro release clause, but the La Liga club want to pay in instalments.
Felix's transfer would be the fifth most expensive in history behind Neymar, Kylian Mbappe, Philippe Coutinho and Ousmane Dembele.
He made his senior debut in August and score 15 goals last season.
Felix would also become the second-most expensive teenager following the 180m euros paid to Monaco by Paris St-Germain for forward Mbappe in 2018.
"Atletico Madrid submitted a proposal for the acquisition of [Felix] for a total amount of 126,000,000 euros which is being analysed," Benfica said, in a statement to the Portuguese stock market.
The former Porto youth player made his international debut against Switzerland in the Nations League semi-final this month.
He scored a hat-trick against Eintracht Frankfurt in the Europa League in April, becoming the youngest Benfica player and the youngest Portuguese footballer to score three goals in Europe and the youngest player ever to do so in the Europa League.