That’s according to a report from Portuguese newspaper Correio da Manha.
Attacking midfielder Felix, 19, has scored four times in nine appearances this season.
Reds boss Jurgen Klopp said earlier this month that it was unlikely his side signed anyone.
But it seems that Liverpool may be trying to bolster their already-strong attacking force.
Felix has been tipped by experts to be one of the next big forces in European football and has been linked with an abundance of top clubs in the past.
The bid of £61m was reportedly rejected immediately by Benfica.
The player has also signed a recent contract extension, with a buyout clause of £105m, way above Liverpool’s bid for him.
The Merseyside club have been linked with a number of names this month, including RB Leipzig forward Timo Werner.
Werner would join up with former team-mate Naby Keita if he were to join.
Liverpool have also been strongly linked with Lyon attacker Nabil Fekir.
Fekir was on the verge of joining Jurgen Klopp’s team last summer but the move fell through at the eleventh hour.
It appears, though, that Liverpool have turned their attentions to Felix.
The wondered can play in the No. 10 position and would fit the mould of the type of player Klopp is looking for.
The Reds boss will face stern competition, though, as it’s expected that when he does eventually leave, he’ll break the Portuguese transfer record set by Hulk in 2012 when Zenit St. Petersburg paid £60 for him.