Gray's contract expires at the end of the current campaign and a Daily Mail report says that unless there is a last-minute change of heart the Scotland lock will be moving on.
Having lost players like Stuart Hogg (Exeter), Finn Russell and Leone Nakarawa (both Racing 92) and other key players in recent seasons, Glasgow's squad requires strengthening in a number of positions.
They have agreed a deal to re-sign Nakarawa until the summer. The Fijian has been a free agent since being sacked by Racing 92 for returning late from the Rugby World Cup.
Warriors are also thought to have been in talks with Richie Gray - Jonny's elder brother - about a return to Scotland from France where he's been playing for a Toulouse.