Swansea have agreed a fee of £6.2million with add-ons with the Premier League champions for the winger.
The fee could rise to over £8million and the winger is currently holding talks with City over personal terms.
The 23-year-old is keen on leaving Swansea and has told the club that he will not be signing a new deal.
Swansea have signed Valencia winger Pablo Hernandez as a replacement for Sinclair.
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Chelsea legend Didier Drogba has revealed his top 11 Chelsea career moments during his recent interview on Chelsea TV.
The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.