The 32-year-old returned to his boyhood club on loan from Everton in October.
He has been an important part of the team in the subsequent months, and Hasenhuttl appears to want Walcott to stay.
Asked about the matter, Hasenhuttl told reporters: "We are in negotiations with the agent and with him.
"I am sure not only this player, but we will have next season a very, very balanced and mentally strong side, for sure.
"It's not a secret that I was very happy with him as long as he's here now because he did a fantastic job.
"We missed him definitely when he was injured. I like a lot of things on this player.
"Not only his workload, also his mentality, his attitude, his professionalism.
"This is something every team needs to have. It's a player every manager likes to work with, because he was positive always and very, very open-minded for new things and in the end never stopped getting better."