Both clubs were involved in a discussion regarding the Brazil international's move to Camp Nou last summer.
Malcom cost Barca €41million and his slow start has seen a number of transfer and loan links crop up, with Everton originally thought to be front-runners before Marco Silva denied interest.
Chelsea have rejected a player plus cash deal from Barcelona, who have seemingly renewed their interest in signing Willian.
A big couple of transfer windows lie ahead for Chelsea and manager Maurizio Sarri.
Chelsea have scored the least goals (36) out of the top six and it's Willian's contribution that's most concerning.
And due to Willian having 18 months left on his current Chelsea contract, the Daily Mail claim the west London club may be tempted to accept. That Barcelona are also willing to offer cash in addition to the young winger, bringing the valuation of the deal to around £50 million, makes it an appealing prospect.
The Blues are in advanced talks to sign Juventus striker Gonzalo Higuain on loan until the end of the season, who is now on loan at AC Milan.
Defensively Chelsea haven't been too bad in the Premier League - they've only conceded 16 goals in 21 games - but going forward they've struggled somewhat.
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