Manager Antonio Conte has made the signing of a top striker a priority to replace Diego Costa, who is expected to leave Stamford Bridge in the summer transfer window.
Romelu Lukaku was understood to be the Italian's preferred option but the Belgian joined Manchester United in a £75m deal earlier this month.
The Sun says Juventus are unlikely to sanction a move for Higuain after they surprisingly sold centre-back Leonardo Bonucci to AC Milan for €42m on 14 July.
Costa is yet to return to pre-season training at Chelsea and has been left out of the Blues squad travelling to the Far East for a pre-season tour.
Atletico Madrid are reported to have tabled a £26m bid for the forward, even though they are barred from registering new players until January due to a transfer ban.
Costa admitted last month that he was interested in rejoining Atletico, but expressed concern over potentially missing five months of football ahead of the 2018 World Cup in Russia.
"Conte has sent a message saying that he does not want me. If they don't want me there, I'll have to search for a team," Costa was reported as saying by the Daily Mirror.
"To go to Atleti would be nice but I have to think about it. This is a World Cup year and I cannot be not playing for three or four months."
Nemanja Matic, who has been linked with a move to Manchester United, has also been left out of Chelsea's pre-season tour.
The Blues have sold Nathan Ake, Nathaniel Chalobah, Juan Cuadrado, Asmir Begovic, Bertrand Traore and Christian Atsu this summer, while Willy Caballero, Antonio Rudiger and Tiemoue Bakayoko have been the only arrivals.