The contract McCormack signed in the summer of 2011 is set to expire and the Robins have offered the defender a new two-year deal.
The Town captain, 29, has yet to respond but McCrory has his fingers crossed that the player will prolong his stay in Wiltshire.
"I spoke to his agent on Thursday afternoon and I offered a two-year contract with improved terms, but he has not come back to us," McCrory told the Swindon Advertiser.
"Alan McCormack has been an inspirational captain for the club and I think he's a genuine guy, a lovely fella and a good footballer.
"We'd love to see him stay at the club. We hope he stays."
- Sports & Recreation
- Alan McCormack