Patrick Bamford would be ‘more than happy’ to stay on loan at Middlesbrough until the end of the season.
The 24-year-old has started just three games for City since his £6.2million move from Swansea last August.
Mancini accepts he has not given the Great Britain Olympic player much opportunity and could understand if he was frustrated.
Mancini said: "This situation with Sinclair is difficult because I didn't give him a lot of chances to play. He is very unlucky.
"It is my fault, not his fault. A young player like Scott who is a good player deserves to play always.
"For him, it was a really difficult year this year."
When asked if that might mean Sinclair deserves to play somewhere else, Mancini, speaking at his regular press conference, said: "Scott is young and he has good quality but this year was difficult for him.
"I think it is better if he can have another solution.
"If he stays here, maybe, everything can change but I can understand his frustration in this moment because he didn't play a lot of games.
"For me, he is a good player. We have one team. For him, it was difficult.
"I repeat - he did everything well, he worked well, he is a good guy, he deserves to play.
"I can understand when one player can't play often it is difficult."
Sinclair's potential exit could be part of a busy summer at Eastlands as Mancini reshapes his squad following the loss of the Premier League title to Manchester United.
The club have this week been linked with Shakhtar Donetsk's £20million-rated Brazilian midfielder Fernandinho.
Mancini was unwilling to discuss that rumour much and expects this summer's transfer market to be competitive.
He said: "We can talk about Fernandinho. Fernandinho is a good player but he plays for Shakhtar.
"I don't think there are a lot of good players (available) around the world.
"There are also four or five top teams who want to buy good players. It could be difficult."