The 22-year-old’s current contract with Rangers is set to expire at the end of December.
Bendiksen has impressed recently and the Scottish side will offer the midfielder new terms.
McCoist told Rangers TV’s Blues News: “We’ve always known about Thomas’ talent, this isn’t a surprise to us.
“I’m delighted the lad’s now fit and he’s got an opportunity to express himself.
“We’re just pleased he’s back in the swing of things after the best part of two years of injuries. Hopefully that’s all behind him.
“I’ve spoken to his agent myself on a couple of occasions. He is very keen for Thomas to stay, we’re keen for Thomas to stay, hopefully Thomas is keen to stay too.
“Negotiations have already started and hopefully we can get him on a long-term contract.”
