Crouch has been in and out of Stoke's first team this season, sparking rumours of a return to QPR and the possibility of being reunited with manager Redknapp, who he played under at former clubs Portsmouth, Southampton and Tottenham.
However, Stoke boss Mark Hughes outlined his desire for Crouch to remain at the Britannia Stadium on Thursday.
"Mark Hughes is saying that they are looking to give him a new contract," he said.
"He belongs to Stoke. He's a good player, but he's not possible to get. That's not a goer."
"We're not that far short. If we can find another striker in January to add to the ones we've got, that's an area we're looking at," he added.
"In January it is difficult because people aren't looking to let players to go. There will be someone, I'm sure, who can come and help us.
"We've scored goals at home. Charlie Austin is our main goalscorer, but you need goals from all areas - midfielders, wide players. Goals should come from different positions."
Redknapp also confirmed that Mauricio Isla is unavailable for QPR's fixture with West Brom at Loftus Road on Saturday because the 26-year-old has returned to Chile to attend the birth of his child.
