The Bhoys celebrated a third successive SPL title under Strachan's management on Thursday night following a 1-0 win at Dundee United.
His achievements at Parkhead have sparked rumours that he could be spirited away by another club after his position as manager had come in for criticism earlier in the season.
"Gordon has been outstanding in his first three seasons," Desmond told the Daily Record. "He's a great person, a great manager and great motivator. He is a great leader.
"I hope he hangs around forever. Whatever he does, he has a job for life.
"He has shown and proved his credentials. It's for him to stay here for as long as he's motivated."