The goalkeeper's current deal runs out at the end of the season, and reports earlier this week suggested that the 34-year-old had rejected an offer from the Ibrox club.
Alexander moved to Rangers on a free transfer in January 2008, understudying Allan McGregor for much of the time until this season.
Now McCoist has renewed optimism that the former Ipswich and Cardiff shot-stopper will put pen to paper following discussions with Rangers' chief executive Charles Green and head of football administration Andrew Dickson.
"We have had good discussions and I am obviously very hopeful him and his representatives can speak to Andrew and Charles," McCoist told the Rangers club website.
"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 (goalkeeping coach) Jim Stewart so it would be crazy not to encourage someone like that to stay."
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