The former Manchester City midfielder – and boyhood Evertonian – had been critical of the Reds boss in his early days at Anfield.
Barton previously branded Klopp a ‘giant German cheerleader’ and claimed Liverpool were regressing under his leadership.
Two years on and Liverpool are the reigning champions of Europe, came within a point of the Premier League title last season and currently lead the division by six points, ahead of their meeting with title rivals Man City at Anfield on Sunday.
Barton has now claimed the German coach “has a Shankly feel” about him having “lifted the whole city.
“I don’t think Liverpool back in the day [during his playing career] were anywhere near as strong as they are now with the fans and the belief,” Fleetwood Town boss Barton said.
“I’ve been critical of Jurgen Klopp, certainly when I was working for talkSPORT, I didn’t feel they were learning lessons.
“But I think they are the most improved team and his is the most improved coach in the last three years.
“He has that, I dare say, Shankly feel to him.
“He has lifted the whole city and Liverpool really firmly believe.
“I live in the city and I’m just hoping Everton can get on the coat tails and latch onto that energy to improve themselves.”