The winger has become one of the Premier League’s forgotten men since his switch to the Sky Blues from Swansea in 2012, with game time having been hard to come by at the Etihad Stadium.
But Redknapp is ready to give him a fresh challenge with a January swoop.
The Super Hoops boss is keen to add more attacking verve to his squad as he look sot battle against relegation, with a permanent or a loan move appealing to him.
The 25-year-old himself is understood to have no future at City, and will be allowed to leave for the right offer.
Sinclair was once tipped to break into the England set-up, yet the former Swans star’s career has moved backwards over the course of the past two and a half years, with a brief stint at West Brom last season not enough to get him firing once again.
QPR are also chasing Jermain Defoe, who is keen to return to England after a miserable year in the MLS with Toronto.