The Icelander was superb in victory at Stoke City.
Gudjohnsen, on loan from Monaco until the end of the season, scored Spurs' opener then played a superb dummy to tee up the winner for Niko Kranjcar after Matthew Etherington had equalised from the penalty spot.
Redknapp said: "I want to keep him here next year. He's a real top player and he's got fantastic ability. With Jermain Defoe out injured he has got a big part to play.
"The chairman did the deal for him and I don't know the details but we are certainly interested. The rest of the lads like him and they really love playing with him."