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.
