Last season was a breakthrough campaign for Dowman, one in which he made his competitive debut as a 15-year-old and continued to break records from there.
He became the youngest player ever to make a Champions League appearance and then the youngest scorer in Premier League history.
Dowman has kicked on to make an impact this season, too. He starred in the Carabao Cup win over Ipswich, scoring a brace.
High praise: Max Dowman
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In a new advert for Adidas, Messi named ten young players he expects to go on to become future stars.
Dowman was one of those, in what is the latest ringing endorsement of just how exciting a talent the 16-year-old is.
"If Messi, who is the best ever player, says that," Arteta said, smiling.
"His eyes are I think better than anybody else’s. Hopefully he’s right."
Adidas have released the new Messi F50 ‘Futbol y Familia’ boots, marking the Argentine's retirement from international football.
Following Messi's endorsement, Dowman wore those boots on Monday as Arsenal trained ahead of their Champions League match against Lille.
The teenager is expected to be in the squad for Tuesday night's match and Arteta is confident Dowman will step up again if given an opportunity.
Asked what made Dowman stand out to someone of Messi's stature, Arteta said: "That he’s got something special.
"In the few appearances that he had, he’s already done remarkable things. That’s somebody that is touched with a special gift.
"He’s a joy to watch. The way he moves, the way he touches the ball, the way he carries himself, it’s just different. And that’s what makes him unique."