The Sun claimsJuventus boss Massimiliano Allegri is open to letting Bonucci leave after a series of bust-ups between the pair last season.
The defender was dropped for Juve's Champions League round-of-16 first-leg clash with Porto in February as punishment for arguing with Allegri during a 4-1 win over Palermo earlier that month.
Allegri signed a new contract with the Italian champions to extend his stay at the club until 2020 this week and is understood be an admirer of Matic.
Bonucci is reportedly valued at £60m by Juventus, but Chelsea believe they can get him in exchange for £48m and Matic.
Bonucci 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 the defender in a £48m deal last summer.
The Italy international 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.
The 30-year-old also played down his disagreements with Allegri, saying he accepted the coach's decision to drop him against Porto.
"I clarified things face to face with Allegri, I accepted his decision, I will pay for a dinner for the team next week. Things are now even better than they were before," he stated.
"You need to take the positives from anything negative and it brought the group further together."