Celtic appear to have missed out on signing Manchester City striker John Guidetti after failing to beat the deadline.
Jermain Defoe came close to returning to England on deadline day, but Toronto FC are hoping to keep him long-term.
The 32-year-old has been heavily linked with a return to Loftus Road, where he plied his trade during the 2000/01 season.
Crouch has previously worked with Redknapp at Southampton, Portsmouth and Tottenham but it looks like he will be remaining in the Potteries.
Speaking to Press Association Sport outside QPR's Harlington training ground, Redknapp said on Crouch: "No, I don't think anything there [is happening with him]. It is very quiet."
Redknapp, who has already confirmed the signing of Anzhi Makhachkala's Christopher Samba today, also confirmed midfielder Alejandro Faurlin is joining Palermo on loan until the end of the season.
"Ali is going on loan," the Rs boss said. "He wants to go and play and he has got a chance to Palermo so that's good for him. "