Alexander is reportedly set to reject a new contract offer from the club after being asked to accept a 50% wage cut.
Kilmarnock goalkeeper Cammy Bell is a target for Rangers but McCoist is also keen to retain the services of Alexander.
He said: I haven't spoken to Neil. I did hear about the report in one of the newspapers.
"I'm obviously very keen for Neil to stay and I've said all along that we need two good goalkeepers challenging for the number one jersey.
"I don't know if there is any truth in the reports in the newspaper but I still want Neil to stay at club.
"I'll talk to Neil at the beginning of the week and see where we are.
"I don't know the contract details, that's not really my gig.
"From what I've been told, it was in one of the newspapers this morning that he's going to reject it.
"So, if that's the case, I'll have to sit down and hopefully we can renegotiate and get together and have a positive outcome."