Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
The 30-year-old has struggled to cement a starting place since the arrival at Ewood Park of Henning Berg.
After 11 appearances in the Championship this season, Orr was an unused substitute in the 1-1 draw at home to Birmingham, having to make way for 18-year-old Adam Henley.
Orr's deal with Mick McCarthy's side is due to end on January 26.
The veteran defender moved to Ewood Park in January this year after a spell of nearly three years with QPR.