The 27-year-old will be out of contract in a year’s time, which means the club wants to cash in on him.
However, Martin believes that even if Walker-Peters stays, he will retain a top class player for their first season back in the Premier League.
He told the fans' forum: "He's a top player. I don't need to say it. He was brilliant for us last season. Some of the stuff he can do with the ball, I can only dream of.
"We're in discussions with him and he will make a decision based on his career. It won't be the fact that we don't want to keep him or haven't tried to.
"We are trying to keep him here for the longer term. Short term, I hope he's here for the season, whatever happens. It's not ideal for someone to be in the last year.
"I think last season, as Stuart Armstrong and Che Adams showed, if they're all in and they're committed, they can contribute hugely anyway."
Martin continued: "If Kyle ends up staying, which I hope he does, the best case scenario is he signs a new contract and everyone's really happy.
"The worst case for me right now is that he stays and is then on a free next summer, which helps us stay in the Premier League. So it's a win-win in the short term.
"Hopefully, we get the long-term win as well. If he ends up leaving before the end of this window, that means that the club can reinvest in someone else.
"Are we trying to keep him? Yes. Is he desperate to leave and kicking up a fuss? Not at all. He's a brilliant professional and played really well on Saturday.
"While he is here, he will be in contention to play in the team. Then the rest after that is sort of beyond our control. We've done everything we can.
"Phil Parsons and the ownership group have made a big effort to keep him and we've made a big effort in the way that we treat him.
"Then it's down to his decision and we'll respect that. I don't begrudge that and it's not personal, it's about his life and his career."