According to reports, Juventus and Paris Saint Germain are keen on signing the experienced midfielder as well.
Barcelona are reportedly under financial pressure, and they are looking to cash in on some of their fringe players this summer.
The likes of Samuel Umtiti, Philippe Coutinho, Martin Braithwaite and Miralem Pjanic are all expected to be on the chopping block this summer. The Spanish outfit are willing to accept a reasonable bid for the 31-year-old midfielder.
Chelsea could use some depth in the central midfield, and Pjanic will add some much-needed creativity alongside Jorginho and Kante.
The Blues need to improve in the attack in order to win the Premier League title, and Pjanic could help create more chances for the likes of Werner and Havertz next season.
Tuchel is thought to be eyeing up a move for Erling Haaland as well to improve his attack.
The midfielder joined Barcelona only 12 months ago, but he has failed to establish himself as a key player for Ronald Koeman.
It will be interesting to see if the player is willing to try out a new challenge in the Premier League.
A move back to Italy with Juventus could be more tempting for the player because of his history with the Italian club. Furthermore, he could reunite with Max Allegri in Turin.
The Italian manager signed the Bosnian for Juventus in 2016 and helped him develop into a top-class player.
It will be interesting to see where he ends up eventually.