TMZ Sports talked to the former NYC mayor (and Donald Trump's attorney) in the city on Sunday ... and asked him about the president's Tweet imploring baseball to put Rose in the HOF.

Giuliani doubled down on Trump's message ... saying "Charlie Hustle" has more than paid the price for betting on baseball -- a cardinal sin in MLB -- over 30 years ago.

"I've long believed that Pete Rose has been left out long enough to make up for whatever he did wrong. It is a Hall that's supposed to recognize baseball accomplishments. He's one of the best of his era."

FYI -- Rose was a 17x All-Star, NL MVP, 3x World Series champ and has 4,256 hits -- more than any other MLB'er.

Giuliani went on to say the National Baseball Hall of Fame is full of guys who weren't the best people off the field ... but the HOF is about playing ball, and nothing else.

"I would say the Hall of Fame is to recognize great baseball players. Some of them may be moral, some may be average, some may be immoral. I don't think we're telling children to copy their behavior if we say they're great baseball players."

"So, it gets a little silly when we use it as a justice system."

It's a long shot, but Rose's standing within baseball could be changing ... 'cause just last week, he petitioned MLB commish Rob Manfred and requested reinstatement.