The Belgian is expected to complete a switch to Real Madrid this summer, with Zinedine Zidane making him his top transfer target after returning as manager.
Chelsea want around £100million for Hazard and have already begun looking at potential replacements for the former Lille star.
According to Telefoot, Coutinho is at the top of the Blues’ wishlist as they attempt to replace Hazard’s goals and assists.
The Brazilian has endured a difficult season at the Nou Camp after making a £146m move from Liverpool in January of last year.
He was jeered by fans against Real Sociedad on Saturday and celebrated his goal against Manchester United last week by putting his fingers in his ears.
Barca are open to selling Coutinho when the transfer window reopens, but they want to recoup in excess of £100m.
If a move for the former Inter Milan star fails to materialise, Chelsea are also considering a deal for Lille winger Nicolas Pepe.
The talented 23-year-old has also attracted interest from Premier League rivals Liverpool, Manchester United and Everton.