Chelsea on Thursday turned down an offer from the Catalan side that would have seen Barcelona send Malcom and an unknown sum of money to Stamford Bridge for Willian, according to Jason Burt of The Telegraph.
It's understood the total value of Barcelona's offer is worth roughly £50 million. Chelsea rejected the deal as it falls short of their own valuation of the Brazilian, who has just 18 months left on his contract.
Barcelona were interested in signing Willian last summer until Chelsea rejected three of their bids; the final one in July was believed to be worth £55 million, according to Kaveh Solhekol of Sky Sports.
Willian, 30, has called west London home since 2013 when he arrived from Anzhi Makhachkala. He was a key member of Chelsea's Premier League-winning squads in 2015 and 2017.
Rather than allowing a player of Willian's caliber to depart this month, Chelsea are instead keen to strengthen their squad. The club is reportedly in the attempting to upgrade its attack with the potential signing of Gonzalo Higuain, currently on loan at AC Milan from Juventus.
Meanwhile, it appears Barcelona are ready to move on from Malcom despite signing the Brazilian winger just last summer from Bordeaux.
The 21-year-old has struggled to break into the first team and is thought to be a likely candidate to move this month, whether to Chelsea or another team. Interested clubs might be in a position to sign Malcom at a bargain compared to the £38-million fee Barcelona paid for him.