City are planning to reinforce their attack ahead of next season and have also been keeping tabs on Frankfurt forward Luka Jovic.
Felix has also caught City’s eye in recent months, and the Premier League champions are working out whether they can make a move to the Etihad Stadium possible in the face of serious interest from Europe’s top clubs.
The 19-year-old, who can play on either wing or through the middle, has scored 16 goals in 38 matches in all competitions during his breakthrough season.
Several City players are also believed to be keen to see Felix join the club.
City’s sporting director, Txiki Begiristain, travelled to Lisbon last week to watch Benfica’s Europa League game against Frankfurt, where Felix scored a hat-trick.
Sources have told Goal that Begiristain paid particular attention to both Jovic and Felix.
Given the high level of interest in latter, City are working hard to ensure they win the race for his signature
The youngster is also wanted by Juventus and Manchester United, among others, and City do not want to be drawn into a bidding war, nor pay his release clause, which is set at €120 million (£103m/$135m).
Agent Jorge Mendes is overseeing Felix’s potential transfer and that could help City’s cause.
Goal has learned that Begiristain recently met Mendes to ascertain the lay of the land regarding Felix’s future, as well as several topics regarding current City players who are represented by the Portuguese agent.
In the past, City have offset the transfer fees paid for Mendes clients by allowing him to arrange sales of his other players already on the books at the Etihad Stadium.
That could be an option for City this summer, with Eliaquim Mangala and potentially Nicolas Otamendi open to leaving the club at the end of the season.
But while Begiristain and Mendes have an excellent relationship, that is also the case with the agent and most top sporting directors in Europe.
It was reported in Italy on Monday that Juventus are hopeful of signing Félix by taking advantage of their ties with Mendes, who helped take Cristiano Ronaldo to Turin last summer.
But Goal understands that Juventus have also been put off by Benfica’s desire to receive the full release clause, having had an €80m (£70m/$90m) approach knocked back earlier in April.
City have despatched other representatives to Lisbon in recent weeks, after being impressed by Félix's team-mate Florentino.
The 19-year-old defensive midfielder features prominently on City’s radar, and the club sent scouts to watch him in Benfica’s 4-2 victory over Vitoria Setubal last Sunday.
Goal understands, however, that City have prioritised the signing of Atletico Madrid midfielder Rodri this summer, and that Florentino will continue to be monitored in the short-term future.