The Sky Bet Championship club had wanted the 10-cap Scotland international for their bid to return to the Barclays Premier League.
But the 30-year-old, a free agent, said no and Rangers are now hoping to get him.
Asked if the League One champions had a chance of signing Cowie, McCoist said: "I hope so. Don is certainly a player we have been interested in … It is our job to continue to look out for the best players possible that we can bring to the club and Cowie would certainly come into that category."
McCoist brought new signing Kenny Miller on in the second half of the 3-0 win over Highland League club Buckie Thistle in his side's first pre-season friendly last night.
And he was delighted with the contribution of Miller, who slotted home the Glasgow club's third goal with eight minutes left.
McCoist said: "It was a great finish from Kenny, a really composed finish. But we expect that from Kenny … It is a great start for him.
"I don't have any doubt once we get Kris Boyd back playing in the side he will be exactly the same. "
He added: "I know it was a pre-season game, and I know we made a lot of changes, but at the same time I thought some of our football was more than acceptable. We have to be pleased.
"We didn't want to take a chance with Lewis Macleod or Kris Boyd, but it was important that all of the lads got a run in the side and they did so. I thought they all did well. They will get fitter and stronger.
"I was pleased that Calum Gallagher scored a couple of goals. Hopefully, they will be inspired by working with and playing with guys like Kris Boyd and Kenny Miller."
McCoist is optimistic Boyd will feature in the next Rangers pre-season friendly against Brora Rangers at Dudgeon Park on Sunday, sayiong he is just "couple of days behind everyone else" after surgery on his ankle in the summer.