The England Under-21 international will move from east to west London and would be available for the Championship play-offs should Rangers fail to secure automatic promotion
QPR will sign Ravel Morrison on loan from West Ham next week, Goal understands.
The two clubs have reached an agreement for the midfielder to move to Loftus Road for the rest of the season after a breakdown in his relationship with the Hammers hierarchy.
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Football League rules allow clubs to sign Premier League players on emergency loans in a window that opened shortly after closure of last month's January window.
Morrison was a key player at West Ham earlier in the season but a slump in form has coincided with a series of niggling injuries. The former Manchester United player has not started a match in the Premier League since December.
Manager Sam Allardyce has spoken of his frustration with Morrison, claiming the 21-year-old could have played through his recent groin injury.
Morrison was the subject of strong interest from Fulham last month, but the west Londoners did not table a bid that matched West Ham's valuation.
"We're hoping to take Ravel Morrison on loan from West Ham for the rest of the season,” Redknapp said in his press conference on Friday.
"He's a fantastic talent and could make all the difference. He seems a decent lad and a talented footballer
"He has got to do it now. Hopefully he can come here and do it consistently. I'm looking forward to having him here."