The 24-year old former Burnley man comes out of contract at Ibrox at the end of the season and McCoist is hopeful that he and the club can come to terms on a new deal so he can stay in a ‘Gers shirt and continue to score goals.
"I'm really keen to see him extend his deal and I'm hopeful we can do that," McCoist told the club's official website.
"It's important we get talks underway and with him having said he would like to stay I would like us to sit down with his people and look at it all. I don't want to lose him.
"I know Kyle's had both fans and critics in the past and he is what he is but I've seen a steady improvement and there's a lot more to come.
"He has a very good goalscoring record here. And I think he will get better still. There are plenty more goals and good games to come from Laff and I want them to be here."