Italian head coach Maurizio Sarri replaced Antonio Conte in the Stamford Bridge hot seat ahead of the new Premier League season.
The 49-year-old head coach worked with Higuain at Napoli, which made Higuain a natural target for Sarri.
However, the Argentina striker has moved to AC Milan instead of a move to the west London outfit this summer.
Chelsea FC will now need to look at other targets ahead deadline day to improve their attack ahead of the new season.
The Blues have been linked with a move to sign Bernard on a free transfer but face competition for the Shakhtar star.
Italian reporter Marques gave an update on Chelsea FC’s pursuit of Brazilian midfielder Bernard on a free transfer.
“The player and the agent are very optimistic for the arrival at # Milan, waiting only for a reply from (sporting director) Leonardo,” Marques wrote on Twitter.
“It is the dream of the player and his father since he was a child.
“Chelsea set their ultimatum for Tuesday.
“There is no Inter offer.”
Chelsea FC finished in fifth place in the Premier League table last season to miss out on a Champions League spot.
The Blues were 1-0 winners against Manchester United in the FA Cup final to end the season with some silverware.
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