The 19-year-old has been in stunning form this season, putting him on the radar of the Premier League big boys.
Felix has netted 18 times and provided 11 assists to his team-mates in a breakthrough campaign.
Now Portuguese outlet Record claim City have held a meeting with the parents of the teenager over a possible Etihad switch.
Real Madrid, Juventus, Bayern Munich and Paris Saint-Germain have also been linked with Felix.
The forward has a £100million release clause in his contract and could be on the move this summer.
The reports claim Manchester City director of football Txiki Begiristain watched Felix as he netted a hat-trick for Benfica against Eintracht Frankfurt.
The man in charge of transfers is said to have started a ‘charm offensive’ to bring the wonderkid to the Premier League champions.
Begiristain was actually at the game to watch Frankfurt ace Luka Jovic, according to the report.
City star Bernardo Silva has admitted he would love to see Felix at the Etihad.
He told Sol: “I really enjoyed playing against Benfica in the Champions League.
“It is very good the bet that Benfica has made on youngsters, from Ferro, Joao Felix, Florentino, to Jota, who has played less.
“I wish I could take the youngsters from Benfica to Manchester. They are all very good.”
City are embroiled in a tight title race with rivals Liverpool that looks like it will go down to the wire.
Guardiola’s side know if they win their final two games they will be crowned champions.
City next face Leicester at the Etihad on Monday evening (8pm).
They could seal back-to-back titles if Liverpool lose to Newcastle tomorrow night at St James’ Park.