The former Eagles forward believes the 20-year-old's career could go the way of the Portugal attacker and thinks he will feature prominently in David Moyes' squad this season.
The 20-year-old picked up his first winner's medal with the Red Devils on his competitive debut as they saw off Wigan to claim a 2-0 victory in the Community Shield last Sunday.
And Bright, who spent six years with Palace, says the former Eagles winger can provide the sort of excitement fans at Old Trafford were used to seeing with Ronaldo.
"I've seen a lot of Zaha because of my association with Palace, having done some coaching in their academy and I think he could be like Cristiano Ronaldo," Bright told Goal. "He has the ability to do everything - he's quick, strong and determined. He's Sir Alex Ferguson's last signing, a great gift to David Moyes."
The Ivory Coast-born England international was a vital ingredient in seeing Palace return to the Premier League last season, earning the decisive penalty that was converted by Kevin Phillips.
However, Bright would like to see the new arrival find the net on a more regular basis than the eight goals he notched last season, insisting he will feature heavily in the first-team for new boss David Moyes.
"He needs to add more goals to his game but he has the ability to go past defenders like no one [in England] since Steve McManaman," Bright said. "He's going to be a great asset to Manchester United and I think he'll play a lot more this season than most people think."
Mark Bright was speaking on behalf of Prostate Cancer UK. Sign up to Prostate Cancer UK's Men United email newsletter to be in with a chance of winning a pair of tickets to the Capital One Cup final and to receive exclusive football content. We fight to help more men survive and enjoy a better quality of life. It's Men United v Prostate Cancer. We can win this.