The 19-year-old enjoyed an impressive breakthrough season in Lisbon, scoring 20 goals in the 2018/19 campaign.
City and their neighbours Manchester United have both shown interest in the forward, who has a €120 million release clause in his contract.
Neither club has met that yet, but Record has reported that City have seduced the player by putting a salary package worth €30 million over five years on the table.
Benfica president Luis Filipe Vieira appears resigned to losing the youngster and is said to have told board members that Felix has been attracted by the high wages on offer in the Premier League.
“We sit down with players and they say "president, I can earn €5million, president, do not make me stay here,” Vieira said.
“Joao Felix had a release clause of €60m and we realised after two or three games that we must increase it to €120m.
“But it is Joao Felix and his family who will decide if he stays. If someone bids €120m it is not worth dreaming that he will stay.
“We are trying everything to ensure he stays. But the only way is if we sell him and keep him another year.
“If not, Joao leaves. There is no room to negotiate further. He doesn't want to. How will Benfica negotiate with someone after he is given a proposal of €6m after tax?'”
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