Rose, 78, was teammates with Bench for 12 seasons while with the Reds. Bench, 71, also had a decorated career. The 14-time All-Star and 10-time Gold Glove award winner also won two National League MVP awards, a Major League Player of the Year award, two World Series titles and a World Series MVP.
Bench is widely regarded as one of the best catchers of all time and was inducted into the Hall of Fame in 1989. Rose is banned from the Hall of Fame, a punishment he received for betting on baseball.
"It don't bother me but you know Johnny Bench is one guy who should thank God I was born," Rose said Thursday on the Brian Kilmeade Show on Fox News Radio. "Because he never would have made the Hall of Fame if I wasn't born. ... Because I'm the guy he knocked in a thousand times. You've got guys in front of you, guys right behind you, and you got to be responsible for everybody else involved."
"I'll continue going around the world we live in and telling everybody he's the greatest catcher of all time. I don't get tired of saying that because it's the truth. Now I can't help it the way he feels, but I would think if he's a Cincinnati fan and he cares about the city of Cincinnati, that he would probably want me to be in the Hall of Fame."
Bench told TMZ in August that he wished Rose was eligible for a Hall of Fame induction so that he wouldn't have to answer more questions about it.
Bench said he doesn't think Rose would ever make it into the Hall of Fame.
Manfred announced in 2015 that Rose's lifetime ban on baseball would not be lifted.
"No matter what happens in terms of legalization, there will always be a rule that prohibits betting on baseball. That's the bedrock of our integrity," Manfred said.
"That's the rule Pete Rose violated. Whether [gambling] is legal or illegal, the rule is still going to be there. First of all, it was illegal when he did it. But more importantly, we're always going to have that rule applicable to on-field personnel. It doesn't change my thinking at all."
Rose's 4,256 hits remain the most in Major League Baseball history. He also is the all-time leader in games played, plate appearances and at-bats.
Rose was a 17-time All-Star, three-time batting champion, three-time World Series champion, two-time Gold Glove winner, World Series MVP and regular-season MVP during his career.