Willian has played a key role in Frank Lampard's Chelsea team so far this season, featuring 23 times in the Premier League.
The 31-year-old has lent some experience to a young Blues side that currently sit in fourth spot, six points clear of fifth.
The bid is reported to be worth £20m and comes as La Blaugrana seek to strengthen their attack following an injury to Luis Suarez.
Suarez is expected to be out until May with a relatively serious knee injury and the La Liga giants are assessing their options.
However, in a tough January market, it's believed Barcelona are adjusting their priorities and price-range.
Barcelona are long-term admirers of Willian, whose Chelsea contract expires in the summer.
Since arriving at the west London club in 2013, the Brazilian has been courted by Barcelona on numerous occasions.
Notably, in 2018 the Catalan club were reported to have submitted a flurry of bids for Willian, before signing his compatriot Malcom instead.
There's believed to be a growing number of clubs interested in signing Willian for free come summer.
Barcelona are hoping to edge out the competition by making a late attempt to bring the attacker to the Nou Camp this month.
As it stands, it doesn't appear likely that Willian will sign a new deal at Chelsea and will be leaving in June.
Willian has won two Premier Leagues, an FA Cup and a League Cup during his time in England.
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