The Icelandic striker, who is on loan at White Hart Lane from Monaco until the end of the season, was the architect in Spurs' 2-1 away win against Stoke on Saturday.
Gudjohnsen replaced the injured Roman Pavlyuchenko 36 minutes into the match at the Britannia Stadium and duly scored one minute into the second half and had a hand in Niko Kranjcar's winning goal for Spurs.
"I want to keep him here next year," Redknapp said.
"I am glad we have got him because every day he comes into training and he is worth watching. Believe you me, he is a fantastic footballer. Technically he is top drawer.
"You don't play for Chelsea and Barcelona if you are not a great player. He is a fantastic footballer in my opinion.
"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."