The 23-year-old, who bagged eight league goals for the Swans last season, alerted Robert Mancini’s side after he announced earlier this week that he will not be signing a new contract at the Liberty Stadium, and is likely to move to the Etihad with Adam Johnson's departure freeing up a spot in the squad.
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But Jenkins is keen to make sure Swansea get the right fee, especially after seeing Steven Fletcher and Matt Jarvis leave Wolves for more than £10 million each.
"When you look at Robin van Persie going for £25 million and there are a couple of players going from Wolves for large sums of money," he told Sky Sports News.
"Scott is a very good young British player and we expect that if any bid is likely to go ahead we've got to get the value that is right."
New Swans manager Michael Laudrup has already made transfer plans should Sinclair leave, with Valencia winger Pablo Hernandez confirmed as a target for the south Wales club.
"I think that one has been publicised with Hernandez and Valencia,” Jenkins added. “That one's ongoing.
"Again, it's something we'd like to conclude as soon as we can but these things do take time.
"But we have got a few other options we're looking at to make sure we don't get caught out between now and the transfer window ending."