Barca are making the midfielder available this summer after a disappointing first season in Spain following his summer arrival from Juventus.
The Catalans wish to set up a swap deal involving Jorginho, 29, in exchange for Pjanic.
The midfielder has revived his Blues career under new manager Thomas Tuchel and become a mainstay for the Champions League and FA Cup finalists. His current deal runs to 2023.
Pjanic, meanwhile, has struggled to make an impact at Barca since arriving last summer from Juventus in a swap for Arthur Melo. The 31 year-old has managed just 17 appearances for Barca in the LaLiga this term.
- updated May 12