The Mirror reports that Villas-Boas is ready to make a staggering £20million bid for the highly-rated teenager.
Barkley has only featured in a handful of games for Everton, but has impressed both Chelsea and Manchester United.
Villas-Boas is keen to complete the signing of Barkley in the January transfer window, but the Blues will face competition from Manchester United.
United manager Sir Alex Ferguson has reportedly made a personal check on the 17-year-old.
