The Sun says Blues boss Antonio Conte will move quickly for the Chilean as he seeks to continue his assault on the Premier League.
Buoyed by the massive payout after selling Oscar for £60m, the Chelsea boss will lodge an initial offer of around £34m.
But Bayern are likely to reject that and will hold out for closer to £40m.
Conte can be confident of luring Vidal to Stamford Bridge, if a deal can be reached with the German giants.
In three years under Conte, Vidal became one of the world’s best midfielders.