The Blues boss has also admitted that when he has a fully fit squad at his disposal then McSheffrey is unlikely to command a regular place in his starting eleven and would therefore benefit from what would probably be an initial loan spell with the Championship outfit.
"There is an interest from Sheffield so we'll just have wait and see what develops," McLeish has said.
"We are prepared to let him go because he would be playing regular first team football."
McSheffrey has made just three starts for Blues this season, two in the Carling Cup against Southampton and Sunderland and one Premier League match at Hull City.