The 23-year-old recently told Swans chairman Huw Jenkins and manager Michael Laudrup that he would not sign a new deal at the Liberty Stadium, and with less than a year to run on his current deal he was widely expected to leave before the transfer window closes on Friday.
City were understood to have made an initial bid of around £5million, but Swansea were keen for a higher offer as Chelsea will get a percentage of any fee due to a sell-on clause inserted when Sinclair moved to south Wales in 2010.
City have now returned with an improved offer, but it is understood it has been turned down by the Swans - who are determined to have their valuation of the player met.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.