The former Chelsea striker has been restricted to just two starts in the Premier League this season and the 23-year-old has not made an appearance for the Citizens since September.
Sinclair, who scored 36 goals in 91 appearances for the Swans, has found it difficult to dislodge City’s first-choice strikers Sergio Aguero and Carlos Tévez.
However, despite a lack of playing time, the England Under-21 international is relishing the chance to learn from his team-mates and become a better player, vowing to seizing any chances to impress in Roberto Mancini’s first-team.
“I really enjoyed my time at Swansea and was playing regularly from the word go but I just felt the time was right to move on,” said Sinclair.
“It really hit me that I’d joined the champions when I signed my contract at the Etihad Stadium and it flashed on the screens that we’d drawn Real Madrid in the Champions League.
“This is why I came here, to play with the best and be in a world-class team and, as a result, develop into a better player.”
He added: “I’m just looking forward to playing in any games.
“All I can do is try to make an impact when the opportunity arises.”
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