It is believed that the shot stopper has turned down the recent contract offer from the Ibrox side, but the Light Blues boss wants a sit down with the experienced star.
Rangers are also lining up Cammy Bell, although McCoist has insisted that the Killie keeper is not seen as a straightforward replacement for Alexander.
"I haven't spoken to Neil about his contract today but I'm keen for him to stay," he said. "I'll chat to Neil this week and see where we are.
"I have said all along that we need two good goalkeepers challenging for the No.1 jersey. 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 that said 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."
And, despite describing himself as something of a traditionalist, McCoist has admitted that his pragmatic side has come to the fore as discussions over renaming Ibrox have gathered pace this weekend.
While the Rangers manager wants assurances that there will be consultations with the club's support before anything concrete takes place, he does understand that it is a viable option.
"The most important thing is the fans' views are taken on board because it's such a controversial topic," he explained. "No matter what happens, people will not be happy.
"All I'd hope for is the majority are happier. If it's the more popular decision to rename it, I hope it'll be the most positive.
"I'm not sure it's an acceptable trade-off keeping Ibrox in the name but it would be the least I'd look for. A big part of the traditionalist in me would say leave it alone – but I totally understand the chance to raise income."
Of more immediate concern, is the performance of his side against Clyde at the weekend.
And with a 4-1 win there was little for McCoist to quibble about.
"The level of goals was great last week but it was even better this time," he said. "The first two were good but I thought David Templeton's two strikes were fantastic and would have graced any level.
"Andy Little is the man in possession of the striker's jersey. Wherever he plays he will make something happen.
"He's very powerful and strong. Get him in a position to score and he will."