Neil Lennon named the Scotland boss as a sounding board last week when he revealed that he occasionally wonders whether he has taken his team as far as he can.
While Strachan, who left Parkhead of his own volition after four largely successful seasons in charge, declined to reveal personal details of any conversations, he also said that such top jobs like Celtic have no set shelf life, and managers need to maintain their own motivation.
"I don't think there is [a shelf life at Celtic]," said the Scotland boss. "I think it is how you feel yourself, are you still enthusiastic about any job? Do you see light at the end of the tunnel? Do you see progress? Are you enjoying it?
"I just did what I thought was the right thing for my family at the time. But I did enjoy it, it was great fun. I didn't realise what good fun it was until I wasn't working.
"And I like not working, by the way. I wasn't sitting about the house. In those top jobs, every day is something different. It makes you feel alive."
Strachan has become an ad-hoc consultant for his former charges, as they negotiate the stresses and strains of management. "I speak to ex-players six, seven times a week and it is great," he said. "They are all starting to get into coaching now: they hated it at the time, but they want to be coaches now.
"They are a bit like me - Howard Wilkinson was always my Samaritans call. I have not seen what Neil has said, but there are six or seven people a week that I speak to and it would be wrong for me to speak about any private conversation."
Occupying Lennon's mind presently is a revenge mission against Aberdeen at Pittodrie on Tuesday. The Northern Irishman said he sensed there would be a renewed title challenge from the Pittodrie side next season, but admitted his players have a point to prove after their 2-1 Scottish Cup defeat at Parkhead.
"I like Aberdeen as a club," said Lennon. "I like their history and I like the city. When they are going well they have a fantastic support.
"In the absence of Rangers, it is important somebody else takes on the mantle. They are starting to do that now.
"Peter Pawlett I really like, I think he is one of the best young Scottish players certainly in the Premiership anyway.
"They are building and improving the squad so I don't see why not [they couldn't challenge next season].
"But obviously they turned us over a couple of weeks ago so there may be a little bit more edge to the game which will be good. Our boys will want to rectify what happened last time."
Lennon is bracing himself for a warm welcome from the locals in a fixture where prank fire alarms in the lead-up to the match have become a regular occurrence.
"Three or four times that has happened so we will make our feelings clear to the hotel," said Lennon. "As long as they [the fans] turn on me and not the players then I don't mind."