Rednapp confirmed he was trying to sign Jenas and Andros Townsend from former club Tottenham on loan.
Jenas, who has been on loan at Championship side Nottingham Forest, then arrived in west London and confirmed the plan was to sign an 18-month deal.
He told reporters: "That's initially. I am fit and ready to go, it's a top club and I am confident the manager can make sure the club stays up.
"I know Harry well, spent a lot of time with him at Tottenham and know him well enough.
"It's a top club, has some good players and not in that bad a position. They're four points off safety and can definitely claw that back."