It is understood his current contract is set to expire in the summer of 2022.
Asked whether he had made it clear to Vestergaard how much he wanted him to stay, Hasenhuttl replied: “I think he feels at the moment, as a leader on the pitch.
“When he performs well and shows the form he has shown after the summer break, where he was physically very strong, then he can be definitely one of the better centre-backs in the Premier League.
“This is very helpful for us and he knows this. I think in the end, he knows that we are happy he is here.
“We didn't always have such a good time together. He was also struggling, like we all have during these two-and-a-half years since I've been here.
“But especially this season he has shown some very good qualities and has developed his game massively. He still knows that we want to have him here.
“We are in negotiations with him and, hopefully, we will find a solution that is best for both of us."