Jurgen Klopp's side are out of contention for the top-flight title, but the Merseyside giants currently hold a one-point advantage over third-placed Manchester United, who face Crystal Palace on Monday night.
Barton has previously been critical of Liverpool's performances under Klopp, but the former England international has suggested that he has been left impressed by the club's recent form.
The 35-year-old told talkSPORT: "Liverpool are up to second in the table, they are pushing on now in the Champions League and it is looking like it could be a good season for Jurgen Klopp and Liverpool. Such has been Liverpool's fall from grace - it has been over 28 years since they last won a title - to finish second is huge. It is a sign of progress.
"Are they getting nearer to winning the Premier League? Well, you would have to say yeah. They are still a number of points behind Manchester City but isn't everybody this season? City have been exceptional."
Liverpool have won 11 of their last 15 matches in all competitions.