Chelsea boss Antonio Conte needs to find a new midfield signing next month, with Oscar and Mikel John Obi both set to move on.
Vidal and Conte worked together a Juventus and the Chile international is emerging as a major January target.
AS says Chelsea are willing to offer €50 million to convince Bayern to sell. Vidal joined Bayern last year for €37 million.
This season, Vidal has played 21 games, scoring three goals and producing two assists.