His performances have attracted interest from United and Barcelona, but TMW claim the Premier League club are lining up a substantial bid to secure his services.
Willian has recently commented on the transfer rumours, but since he was on global duty with Brazil, he refused to go into detail on his future.
Willian is tied to Chelsea for another two years but fell out of favour last campaign under Antonio Conte and played a string of matches coming off the bench.
The Brazilian scored six goals while assisting eight. The Brazilian, who just crashed out of the FIFA World Cup is reportedly being closely monitored by the Barca board. Willian though, is highly sought-after in this summer's transfer window.
Willian is therefore wanted following the departure of Andres Iniesta and the Barca hierarchy also want him to link up with compatriot Philippe Coutinho. But, Barcelona are the clear front-runners in his pursuit.
It looks highly likely that the winger is doomed for a move away from West London and the Blues could be intent on utilizing this situation in their favour and raise their asking price.
Is it that way to Barcelona? Willian's arrival from Chelsea would thus, enable the Barcelona boss to bolster his attack considerably.
According to the report, Argentina star Messi and Uruguay striker Suarez want a complementing player who can deliver the ball quickly into the centre of the pitch from the wing so they can do their thing.