The Champions League winner is out of contract next summer, and previous reports from Diario Sport claimed the Catalans were interested in making a move for him.
The Italian international has remained as a key figure at the Premier League giants despite their change of manager from Thomas Tuchel to Graham Potter.
His agent, Joao Mendes, previously hinted at the 30-year-old preferring to extend at Chelsea, rather than push for move to Barcelona, but the situation remains unresolved.
As per fresh reports from Sport, Mendes has already met with Barcelona officials to discuss a potential move next year, with a January deadline set over his future plans.
The 30-year-old can agree a pre-contract deal with a non-English club from the start of 2023, and he is expected to make final decision on his next move during the winter window.