Manchester United manager Jose Mourinho reportedly retains an interest in Willian and will push ahead with a £60m offer for the Chelsea forward.
Mourinho, who brought the Brazil international to Stamford Bridge from Shakhtar Donetsk five years ago, is said to be after at least one attacking player this summer.
According to the Daily Mail, United intend to pounce on Willian's uncertain future at Chelsea by making an approach during the current transfer window.
Willian will be offered a bumper contract by the Red Devils to help force through a move, with the 29-year-old already unhappy after being demoted to the bench for large spells last season.
However, the former Shakhtar ace was still named Chelsea's Players' Player of the Year for 2017-18, and it is claimed that the Blues will be reluctant to offload to a direct rival.