The La Liga giants have renewed their interest in the Brazilian star after they reportedly had a £55million bid rejected over the summer.
According to La Sexta, Barcelona are now preparing a January swap deal for the 30-year-old.
The European giants were linked to Willian earlier this summer, but they were not willing to match his £70m asking price.
Reports in Spain have suggested that the club has already held talks with the Brazilian's representatives.
But Ernesto Valverde's side would also have to offer Chelsea a large fee following Malcom's slow start to the season.
Malcom only signed for the Catalan giants in the summer, but he has failed to live up to expectations and has played just three times.
Following his £36million switch from Bordeaux, the 21-year-old is yet to start a single game under Valverde.
The Brazilian allegedly wants to leave the club already and his agent has been in talks with several clubs.
Premier League rivals Arsenal and Tottenham have both indicated their interest in the out-of-favour forward.
But it's a different story for Willian, who continues to be a pivotal figure in Maurizio Sarri's squad at Stamford Bridge.
The Brazilian has made over 175 appearances for the club since he joined them from Anzhi Makhachkala in 2013.
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