McSheffrey is resigned to leaving St Andrew's after making just five appearances in the Premier League this season and revealing Birmingham boss Alex McLeish is prepared to let him go.
He could be offered an escape route by the Blades as Blackwell looks to build up a squad capable of maintaining a push for promotion from the Championship.
"Gary is a player I have always liked and I am keen to get more depth in my squad," said Blackwell.
McSheffrey joined Birmingham City in 2006 from Coventry City and had a brief spell on loan at Nottingham Forest last season.
Sheff. Utd 6/5, Draw 9/4, Middlesbro' 12/5