The Midlands club were in talks over a deal to bring in the 25-year-old, who has struggled to break into City’s first team since a transfer from Swansea in 2012.
Sinclair is keen to move on and kickstart his career, with a number of clubs interested in his signature, but Lambert told reporters on Friday the deal is dead in the water.
“That???s dead – it’s not going to go anywhere. We just couldn???t really do it,” Lambert said.
Sinclair has made just three starts for City in over two and a half years, spending a portion of last season on loan at West Brom, and only 19 appearances overall.
He began his career at Chelsea and spent time on loan at six lower division clubs before signing for Swansea in the Championship for ??500,000 in 2010. He was an instrumental part of the side that won promotion in 2011 and then survived in the Premier League under Brendan Rodgers the following year.
After 36 goals in 91 appearances, former England U21 international Sinclair left Swansea for Manchester City but has rarely been close to the first team.