The London Evening Standard says Chelsea boss Antonio Conte will make another attempt to sign Bonucci to replace the departed John Terry, after failing to convince the Italian defender to move to Stamford Bridge last summer.
Bonucci, 30, was part of the Juventus team that lost 4-1 to Real Madrid in the Champions League final on 3 June. Chelsea were reported to be interested in signing Bonucci in a £48m ($62m) deal last summer.
The Italy defender said in an interview in March that he would only leave Juventus if the club decided to sell him.
"I don't know if [Juventus manager Massimiliano Allegri] will go to the Premier League, but I'm owned by this club and the club will decide whether or not to sell me. I hope to honour the contract," Bonucci was quoted as saying by Goal.
Chelsea are also reported to be monitoring Roma defender Antonio Rudiger, although the German centre-back has been closely linked with Inter Milan.
Meanwhile, Van Dijk's transfer to Liverpool has run into trouble with reports suggesting that Southampton will report the Reds to the Premier League over an alleged illegal approach for the defender.
The Daily Mirror claims the centre-back was flown to Blackpool for an unauthorised meeting with Klopp, who is then reported to have continued to have kept in touch with the player trying to persuade him to join him at Anfield.
Southampton are reported to be holding out for a transfer fee of £60m for Van Dijk, as they are obligated to pay 10% of any fee they get for the defender to Celtic. The Saints signed the 25-year-old from the Scottish club for £13m in 2015.