A £800k offer for the 29-year-old former Bradford and Burnley forward was tabled and reported to have been turned down.
However, Blues boss Steve Bruce has stated City are still considering the proposal and that talks remain open.
Blake has made just 13 appearances since joining from Burnley and is considering his options at St Andrews.
"We have had an offer for Robbie Blake from Leeds which we are considering and talks are ongoing," said Bruce on the club's official website.
"The fee hasn't been agreed yet and there's no time limit or anything like that.
"Robbie's done really well for us but his frustration is that like a lot of footballers he obviously feels he wants to play more.
"Someone like Leeds would give him the opportunity where he would probably play every week."
Blake started his career at Darlington and has also played for Nottingham Forest.