Those at Anfield agreed to part with Brazil international playmaker Coutinho in the winter transfer window of 2018.
Coutinho had been a key part of Jurgen Klopp’s plans, but was allowed to move on and those he left behind have become serious contenders for Premier League and Champions League crowns.
Domestic rivals at Stamford Bridge now find themselves in a similar position when it comes to Belgium forward Hazard.
He is yet to commit to fresh terms and continues to be heavily linked with a move to Real Madrid before entering the final 12 months of his contract.
Barnes believes Chelsea could benefit from sanctioning a summer sale, with Liverpool having shown that there are positives to be found from moving on a talismanic presence.
The Reds legend told beIN Sports: “I think they need to get away from Eden Hazard.
“I think Liverpool, when Coutinho left, they were a much better team.
“I think Hazard influences the team so much that anywhere he goes you have to give him the ball.
“They’ve got good players and they can’t show their worth.”
Barnes added: “When Coutinho left, as much as he was the best player, the team became a better team.
“And I think Hazard dominates that team so much that every time they get the ball they have to give it to him.
“I think they’ve got to get away from Hazard because they’ve got good players, like Willian and Pedro.
“But they’re not able to show what they can do because it’s all about Hazard.”
Chelsea’s reliance on Hazard is understandable.
He has contributed 19 goals and 13 assists to the Blues cause this season, helping Maurizio Sarri’s side to a top-four finish in the Premier League and into the semi-finals of the Europa League.