It is understood that the 34-year-old fullback has been in talks with officials from the Etihad Stadium over a move to England in the recent weeks and a deal said to be worth around £5m could come into conclusion in the upcoming weeks.
The Brazilian defender earlier last week admitted that one day he also would like to play in England and he is now keeping all his options open.
He said: "Last year I turned down many offers from the Premier League because I felt I had to go to Serie A."
"There is a great defensive culture, and to go and play in England you have to know how to defend well. I hope that one day I will go there. Who knows? We'll see."
The 34-year-old has only one year remaining on his contract and cashing on him in this Summer would be a wise decision for the Old Lady.
Manchester City are without a properly recognised right-back after releasing both Pablo Zabaleta and Bacary Sagna at the end of their contracts.
They have been also linked with Tottenham Hotspur's Kyle Walker and now could replace both the players swiftly with these two signings and end their dilemma in the full-back position.
Pep previously worked together with Alves at Barcelona during his four years in charge at the Nou Camp and both of them has a very good relationship.
During their time together at Camp Nou, Alves and Pep won 14 major titles including three La Liga titles and two Champions League trophies.
The Brazilian fullback knows the Pep's style of football more than anyone and should the deal happen, it will be a huge boost for the Spaniard coach who is eagerly waiting for success in the Premier League after finishing third in his first season.