The Northern Ireland winger is out of contract at the end of the season but Rovers chief executive John Williams confirmed the club were keen to keep him at the club.
"We're aware that Keith Gillespie's contract is running out," said Williams.
"So we will be sitting down with him and his agents at Christmas."
The former Newcastle winger is set to face Walsall in Wednesday's Worthington Cup clash as Rovers begin their defence of the trophy.