Manager Terry Butcher revealed the former Leicester player would hold talks with Swindon in the coming days.
Butcher told BBC Radio Scotland's Sportsound: "It looks like Lee Cox will leave on Monday. We have agreed a fee with Swindon. It's up to Swindon now."
Meanwhile, Butcher revealed influential midfielder Andrew Shinnie could miss the rest of the season after tests showed he needs an operation on his broken foot.