Celtic are understood to be in talks with Howe, who has emerged as the front-runner to succeed Neil Lennon.
Alexander had six months playing in the English Championship under Howe, who is six years his junior, but never started a game, coming off the bench in the latter stages of 15 matches.
The then 39-year-old departed Burnley in the summer to return to Preston despite having another season left on his contract but Alexander understands Howe's reasoning.
"He finished my career at Burnley to be fair, but he is a fantastic manager," the 49-year-old said.
"It was a difficult time for me and we certainly had our issues. I was fighting to be in that team, I was the club captain, but he had plans to change the team. And it needed changing.
"I only had an understanding of what he was going through when I became a manager myself. I look back and I have made the exact same decisions myself with players since that he made with me.
"I remember when I first got a manager's job, he sent me a nice message as well. I have no issues going forward but it wasn't the best time for me on the pitch.
"But you could see the quality he had and he has proved that at Bournemouth right through the divisions.
"Whichever club he goes on to manage, he will do a fantastic job."
Howe has developed a reputation for preferring younger players.
"He certainly did in my case," Alexander laughed. "Mind you, everyone was younger than me at that stage.
"His reputation is not a false one, it's built on results and success at different levels.
"It will be a different challenge for him. He possibly found Burnley a different challenge to what he had at Bournemouth, and wherever he goes next, and certainly Celtic, will be a different challenge to what he has had before.
"But quality managers like him always adapt to the situation and find the best.
"He has worked with younger players in the past, I think he had to at Bournemouth in the early days, but he had good success with them and has kept that idea going.
"But his record is proven and he has worked at the top level in the Premier League in England, keeping Bournemouth up until last season.
"Whichever club employs him next, and he decides to go for, you pretty much know he is going to do an excellent job.
"But obviously the parameters at Celtic and Rangers are pretty extreme, so that's a challenge for any manager that goes into one of those jobs."