The Catalan giants have identified the star as their top transfer target this summer and have already had two bids rejected after new Blues boss Maurizio Sarri signaled his desire to keep hold of the 29-year-old in London.
The Blaugrana turned their attention to Willian after their move for Antoine Griezmann failed to come to fruition, where their initial bid of £50m for the Brazilian was swiftly followed up by an offer of £53m, both of which were rejected by Chelsea who are understood to value Willian at closer to £70m.
According to Sky Sports, Barcelona has now launched a third bid in the hopes of securing a deal, where talks are still ongoing between the two clubs and Willian's representatives.
Manchester United, however, is prepared to offer €60m as manager Jose Mourinho eyes a reunion with the 29-year-old, according to Sport (via Sport Witness), but the Blues are likely to be resistant to allowing another one of their star players to move to a domestic rival.
The report fails to make clear whether United's offer has officially been tabled, but the Red Devils have long held interest in the winger and they could be biding their time for Barcelona's approach to fall through.
Willian was determined to leave Stamford Bridge this summer should Antonio Conte had stayed at the club beyond the summer, with Barcelona understood to be his first choice, but the Blues are now hopeful that Sarri's arrival can encourage him to stay.
The 29-year-old has made 236 appearances for Chelsea since joining the club in 2013, where he notched 44 goals and 39 assists.
In other news, Barcelona is reportedly in negotiations with Arsenal over the potential departure of midfielder Andre Gomes after the Spanish giants deemed the Portugal international to be surplus to requirements.