The Spaniard, a two-time world champion like Verstappen, has not won a race since he was at Ferrari a decade ago but at the age of 41 is rolling back the years with a car that is taking the fight to dominant Red Bull.
Alonso was on provisional pole until Verstappen pulled out a jaw-dropping lap for the ages and seized the top slot, with the Aston Martin driver still set to start alongside on the front row.
The Spaniard jokingly suggested at a press conference that championship leader Verstappen could maybe help him out on Sunday with a poor start.
"I think we need the help from Max, but we cannot... take it for granted that all three cars will finish the race with no issues. This is Monaco and it's going to be demanding," said Alonso.
Asked jokingly whether he might be willing, Verstappen chuckled.
"I mean, I like to see Fernando win but I also like to see myself win. It's a tough one, I'll think about it," he replied.
Verstappen, 25, said 2005 and 2006 champion Alonso had always been a driver he admired.
"I grew up watching Fernando in F1 and I liked his style and for him to still be here at 41 it's very impressive and I think it's a great example for people out there," he said.
"If you stay committed and believe in yourself, believe in the opportunities that come to you, then you can show something like he's doing right now. But, of course, you need also a lot of natural raw talent with that."
Alonso has had four third-place finishes in five races since he joined Aston Martin this season and Sunday should see him go at least one better.
He said it was good also to show his speed to a new generation of fans attracted by the Netflix docu-series 'Drive to Survive' but who may have only seen him in less competitive cars.
"Maybe... they only saw me fighting for Q3s or something like that or retiring in the race with some smoke at the back," he added. "So, now I think they are surprised that they see me fighting a little bit towards the front."
