United are not against the idea of selling the Italian full-back, provided their asking price of £18m ($23m) is met.
Darmian was signed by former United boss Louis van Gaal in 2015 to play at right-back, but the Italy international featured prominently at left-back last season in the absence of the injured Luke Shaw.
The 27-year-old started 15 league games for the Red Devils last campaign and played the full 90 minutes of the club's Europa League final victory over Ajax.
Darmian said he was unsure of his future at United after Italy's 3-0 friendly win over Uruguay earlier this month.
"Surely this is not the moment to talk about the transfer market," he said. "I wouldn't know what to answer.
"I have a contract with Manchester United, so let's see what happens.
"It's well known that playing at Manchester United brings with it a lot of competition so you need to accept the choices made, keep working as I did, and then I have reaped the benefits at the end of the season.
"We have won a Europa League and this is what makes me go forward, this is my mentality and I will keep going this way."
City boss Pep Guardiola is expected to make a formal approach for Alves in the coming days after releasing both Pablo Zabaleta and Bacary Sagna at the end of last season.
Guardiola worked with Alves before at Barcelona, with the pair winning three La Liga titles and two Champions League titles together at Camp Nou.