The Spanish champions are understood to have made a number of bids for the Brazilian winger, the latest of which could be worth up to £65m.
Willian looks set to leave Chelsea this summer following the arrival of new boss Maurizio Sarri, who is understood to be open to selling the 29-year-old should a suitable offer arrive.
Manchester United have also been heavily linked with a move for Willian, and the Daily Mail reports that Barca are concerned they could miss out on his signature to Jose Mourinho's side.
Both clubs are able to offer Champions League football, whereas Chelsea will compete in the Europa League next season following their fifth-place finish last term.
Willian made just 20 Premier League starts for Chelsea last season, but still managed to score 13 goals and set up nine more across all competitions.