Chelsea are reportedly the favourites to sign free agent Bernard ahead of the 2018-19 campaign.
Bernard is currently without a club following his exit from Shakhtar Donetsk at the end of last season.
A number of clubs - including West Ham United and Leicester City - have been credited with an interest in the 25-year-old over the last couple of weeks.
However, according to Globeosporte, Chelsea are the favourites to land Bernard on a free transfer, with new Blues boss Maurizio Sarri said to be an admirer of the former Shakhtar attacker.
Bernard, who is a 14-time Brazil international, scored 28 times and registered 35 assists in 157 appearances for Shakhtar between 2013 and 2018.