Blues boss Antonio Conte knows Vidal well from his time in charge of Juventus, and according to journalist Manuel Veth, a reunion is on the cards at the end of the season.
It is claimed that a deal will hinge on the future of Schalke midfielder Goretzka who could leave the Bundesliga club on a free transfer at the end of the season, with Bayern leading the chase.
If the Bavarians do complete a deal, that will clear the way Vidal to head to Stamford Bridge.
"Sense has been for quite some time that Bayern had nailed down Goretzka," he wrote on Twitter. "We will likely find out as early as tomorrow if the deal has in fact gone through.
"Goretzka to Bayern would also explain Arturo Vidal's link to Chelsea. From what I understand it is likely the Chilean will be re-united with Conte next summer if/when the Goretzka deal goes through."