Zenden current contract expires at the end of the season, but Bruce believes the former Liverpool and Chelsea star still has a lot to offer.
The 34-year-old has made 21 appearances in the Premier League this season, albeit mostly as a substitute, and Bruce is keen to keep him on Wearside.
"We'll look at a contract for him in the next week or so," he said.
"I've already had a little conversation with him because his physical stats haven't deteriorated at all since the start of the season.
"In fact he's done very well. He's still got a lot to offer this club.
"He's a great asset for the club and we'd like to hang on to him for longer, which is why we're looking at a new contract for him."
Zenden has yet to decide if he will sign the new deal on offer as it depends on how much he will be playing next season.
The midfielder admits it has been frustrating playing a bit-part role as he wants to be a regular in Bruce's plans.
"The issue is how much a part I have to play," Zenden told the Daily Mail.
"I've played quite a lot this season but some of the appearances have been for the last five minutes, which is not so nice.
"I don't just want to be here to be here, I want to be important as well. I'm having a good time. I don't feel old. I still feel like one of the boys."
