Celtic have recently appointed former Liverpool boss Rodgers as their first-team manager following the departure of Ronny Deila.
Meanwhile, the Bhoys’ Old Firm rivals Rangers are interested in signing Barton on a free transfer in the summer.
The Englishman is on the books of Premier League-bound Burnley at the moment, but his current contract with the Clarets runs out at the end of next month.
Rangers manager Mark Warburton recently told BBC Sport that he wants to recruit the former Newcastle United midfielder on a free contract in the summer transfer window.
Former Rangers boss McCall believes that signing Barton would be a massive coup for the Glasgow giants.
The former Everton midfielder has also claimed that it would be as big as Celtic appointing Rodgers as their manager.
“It would be a massive coup if they could get Joey Barton,” said McCall on BBC 5 live Sport on Friday evening (May 20).
“I think Joey Barton signing for Rangers would probably just be as big (as Celtic appointing Brendan Rodgers),” added the former Rangers midfielder.
Barton may be 33 years of age, but he is still a very good midfielder who would be a great signing for Rangers.