The 34-year-old's deal expires at the end of the season but McCoist was reassured by the former Cardiff player that he could sign a new contract.
McCoist will now encourage negotiations between the player and Ibrox chief executive Charles Green and head of football administration Andrew Dickson.
McCoist told the club's official website: "I spoke to Neil this morning. We have had good discussions and I am obviously very hopeful him and his representatives can speak to Andrew and Charles.
"There have been one or two things written and said in the press - and I'm not sure all of it is accurate to be honest with you.
"Neil has shown great loyalty to the club and he has never, ever been a problem. He's a great trainer and his professionalism is fantastic.
"He works really well with Jim Stewart so it would be crazy not to encourage someone like that to stay."