And the ex-Ayr United and Raith Rovers boss believes his old team-mate deserves to continue as Gers manager due to the massive responsibility he has shouldered in the past four months.
"I met Ally on Wednesday at Murray Park and we had a brief five-minute chat," said the Radio Clyde pundit.
"He seemed like a tired guy to me. He is normally laughing and joking, having a carry on. There was none of that, though, when we met.
"You have to remember this is Ally's first year in management. It would be hard enough to cope with everything that has happened as an experienced manager.
"Ally deserves the chance to prove he is a good manager after all he has been through. He had no chance this season with everything else going on off the park.
"I hope Ally is still the manager next season. He has led the club through all their financial difficulties without anyone to help him."
Speculation was rife yesterday that the legendary goalscorer was set to quit as gaffer after a reported fall-out with new owner Charles Green.
The 48-year-old will not, though, walk away from Rangers despite HMRC rejecting the CVA that was hoped would save the club.
However, it is doubtful if McCoist will be able to work with former Sheffield United chief executive Green and his consortium.
If Green, who has claimed he wants McCoist to remain in charge, sacks the supporters' favourite then it is unlikely he can count on the backing of the paying customers.
And the fans are already behind the rival takeover bid fronted by legendary manager Walter Smith and supported by multi-millionaire businessmen Jim McColl and Douglas Park, who would now have to buy the newco from Green after he got his deal over the line yesterday afternoon.
Dalziel believes Green's chances of success with the Rangers newco on and off the field would be jeopardised without McCoist as manager.
"It shouldn't be a great surprise that, if it is true, Green wanted to replace McCoist," reflected the former Ibrox hitman. "This is the way football is just now, this is the way football clubs are run.
"Look at Harry Redknapp at Spurs this week. He did a phenomenal job at White Hart Lane and still lost his position.
"Nothing surprises me about football any more. Every manager's job has a lifespan. You more or less know when you become a manager that you are going to end up getting sacked."
Dalziel added: "But Charles Green will put enormous pressure on himself if Ally is sacked or walks away.
"He may see a different avenue for a Rangers newco to go down and want a different boss in place.
"But he would live or die by those decisions. If he gets it wrong then the supporters will turn on him.
"Of course, it happens. I think it happens in a lot of clubs. Sometimes a chairman and a manager don't see eye to eye.
"What it all boils down to at the end of the day is that the Rangers manager must get results on the park.
"The saga at Ibrox has taken yet another twist with Walter coming back in and asking Charles Green to step aside.
"I'm not sure if he can stay at Ibrox without the support of Ally McCoist now."