Murray resigned from his post last Tuesday after claiming he had been undermined by the club's owners. He had also been left frustrated in his attempts to strike a deal with Lorraine Johnston and Samantha Twigg for their 52% majority shareholding.
The Trust are concerned about the direction the club is heading in following Murray's departure and are now weighing up an offer.
"The Trust see this situation as an opportunity, finally, for our club to be owned by our supporters," they said. "Much work has to be done and we will aim to keep everyone advised as far as we can."