The former Gers boss, speaking exclusively to Football Insider, admitted he does not think the 29-year-old will pen a new deal even if the Light Blues win the Premiership and qualify for the Champions League.
As reported by the Daily Record last week (Friday, 31 December), Rangers are set to renew contract talks with Goldson as he heads into the finals six months of his current deal.
The Gers will reportedly not sanction a transfer this month, even if it means losing him on a free in the summer.
However, McLeish admitted Goldson may want to follow Nathan Patterson to England.
Discussing Rangers missing out on a multi-million transfer fee, McLeish told Football Insider’s Russell Edge: “That would be the sacrifice. Absolutely.
“The Champions League is not guaranteed. It certainly gives you a better chance when you keep your best players.”
Asked if winning the league, which would see Rangers qualify automatically for the group stages, could convince Goldson to stay, McLeish said: “It’s different nowadays than it was all those years ago.
“We’d certainly have waited to play in the European Cup. I would think that players would be thinking more about their future and the financial side as well.
“Let’s face it. A move like Nathan Patterson’s doesn’t come around every week. Possibly, Connor will be thinking of something like that.
“He’ll possibly look to get back to England. That is if he and his agents feel that he’s capable of playing at a high level in the Premier League.”
Goldson has 193 appearances under his belt for Rangers to date.