Stoke boss Tony Pulis has hinted that a deal for Crouch could be a possibility, and the Hoops are also continuing to pursue West Bromwich Albion attacker Peter Odemwingie, for whom they have had two bids rejected already this window.
Redknapp has claimed that his squad is short on numbers, but is still optimistic of adding the trio, or other targets, to his ranks before Thursday's 11pm deadline.
"We need to strengthen the squad - tonight I had two keepers on the bench because there were no other senior outfield players here," Redknapp said.
"There are one or two lads who are here who want to leave as well, so we went through the numbers tonight and we've probably got about 17 [players] for our 25-man squad. We've got to fill it up a bit.
"We are desperately short in quite a few areas really, we do need some reinforcements. We'll have to see, hopefully we can get some stuff done tomorrow [Wednesday]."
Redknapp was speaking after steering his side to a goalless draw with Manchester City at Loftus Road tonight.