The defender was expected to leave the club before the transfer deadline at the end of the month.
However, no team has made a suitable offer for Walker-Peters, who can leave as a free agent at the end of the term.
Per Daily Echo, Martin said: "I think he's going to be here. I think all the interest that was there and the deals that might have happened have pretty much gone.
"That is unless someone decides really late that they want Kyle. We've offered him a new contract so when the window's shut maybe that will be another discussion.
"If not, he needs to play in the same way he has done, the same way Stuart Armstrong and Che Adams did last year in the last year of their contracts.
"They were fantastic for us and Kyle has been great, so I think everyone's really relaxed about it. He's played really well in the first two games.
"It's a bonus having him here when I think we had all sort of resigned ourselves to him leaving the building."