The Ibrox midfielder poked fun at the Bhoys chief's appearance.
Celtic manager Brendan Rodgers
New Ibrox recruit Barton was asked on Wednesday's Alan Brazil Sports Breakfast show if he had come across Rodgers since moving to Glasgow.
Joey Barton applauds fans as he is substituted
In his response, which drew laughter from both Brazil and co-host Kevin Nolan, a former teammate of Barton at Newcastle United, he implied Rodgers was going through a 'mid-life crisis'.
"No I’ve not managed to run into him yet," Barton said. "The places he goes and the places I go probably differ, with the tan and the teeth and all that.
Rodgers poses for a photo with a fan before the game against Inter Milan
"They’re not the type of establishments I rock up at - I’m not having a mid-life crisis!"
Rodgers was given the right of reply in his pre-St. Johnstone press conference on Friday but said, as quoted the Daily record: "Lots of noise in modern football. Doesn't bother me, I just focus on my job."
It is not the first time in his short Rangers career that Barton's comments have caused a stir in the Green half of Glasgow.
Earlier this summer, the 33-year-old engaged in a war of words with Celtic skipper Scott Brown, who he claimed was 'nowhere near his level'.
Celtic's Scott Brown applauds fans after the game against Hapoel Be'er Sheva
Brown later joked he thought the pair would get on well, given that Barton had previously admitted to being a fan of the Bhoys.
However, the Liverpudlian, who supported Everton growing up, responded by posting photos on social media of a young Brown wearing a Rangers strip.