The Bosnia international striker has earned the reputation of being a super-sub this season, with 18 of his 35 appearances coming from the bench.
He is the club's joint-top scorer this season with 13 goals, but is understood to have grown frustrated with a lack of starts at the Etihad Stadium.
The 26-year-old was linked with a move to Inter Milan in the January transfer window, but with fellow forward Mario Balotelli eventually completing a move to AC Milan, boss Mancini was reluctant to weaken his forward line still further.
Rumours of a summer exit have persisted though and Mancini admits Dzeko may leave the Premier League champions, but he will not let the forward go on the cheap.
"Edin is an important player for us," Mancini told Sky Italia. "At this time we have not spoken about the transfer market as there are still 10 games to go.
"But in June anything can happen. If a player asks me to leave, we will evaluate the situation, this applies for all players.
"Dzeko for me is a great player. In Italy he could score more than 20 goals a season. But he would cost €20million, maybe more."
Mancini also played down a training ground bust-up with Balotelli in the days prior to his eventual departure.
Photographers caught the incident at the club's training ground in January, with the pair having to be split up by members of the City coaching staff.
"Those were lies reported by the tabloids and photographers who were here, because there was absolutely nothing," said Mancini of the incident.
"We were playing a training match, we were playing in opposing teams, he made a foul and I shoved him and sent him away.
"Mario has improved but I think he won't change at all, he will continue to make faults even when he is 30.
"But the important thing is that he understands that he can and should give more on the field, because the best is expected from a player like him every time."