Thompson is thought to have turned down six-figure offers from Championship side Burnley and Coca-Cola League One outfit Nottingham Forest and is holding out for around £1.25 million.
"Celtic contacted me about Barry before the Old Firm game on 2 January, which was eventually postponed," he said. "But I haven't heard from them since, although their chief executive Peter Lawwell is a wily negotiator and it wouldn't surprise me if they came back in again.
"A £1 million offer wouldn't satisfy me, that wouldn't be enough.
"We've had offers for Barry but we've turned them down and I'm expecting more bids from south of the border on Monday morning.
"I want Barry to be happy in his football but he'll only go for the money we think we deserve."