The move is reportedly part of the Antonio Conteâ€™s plan to revamp the squad, despite their run of five Premier League wins in a row, keeping clean sheets in all of them.
The Blues manager is looking at adding the Italian to his squad after the club have said they are willing to listen to offers for Cesc Fabregas.
The 24-year-old is said to be looking to leave the French capital if he does not win any trophies with them this season.
Paris Saint-Germain are third in Ligue 1, three points off Nice who top the table on 29 points.
The West London side will be hoping to beat fellow Premier League rivals Manchester United to the signature of the player.
Since joining the side in 2012 from Pescara, Verratti has won four Ligue 1 titles and has made it to four consecutive Champions League quarter-finals.
The midfielder signed a new five year deal over the summer, but recent comments from his representative Donato Di Campli suggest he could be looking to move away from France.
â€œThe contracts are made and unmade in three minutes,â€ his agent said.
â€œWeâ€™ll see PSGâ€™s aims, Marco is happy to be there, but he wants to win something important. He can not stay in a team that does not win.â€
The move would allow John Obi Mikel to leave at the end of the season when his contract expires.
With Verratti looking to win something significant, a move to a team like Chelsea who have had consistency in top European competitions over recent years could be the deciding factor in bringing him to England.