The Toffees are already thought to be closing in on a move for Yerry Mina from the Catalan giants but are now planning an "ambitious double swoop", according to The Mirror.
The newspaper says that 24-year-old Digne is now "resigned to moving on from Spain" following a campaign that saw him make just 12 La Liga appearances and miss out on the France squad for the World Cup.
Everton's director of football Marcel Brands is said to have abandoned the club's pursuit of Tierney due to his £25m asking price and now believes that he can secure a more experienced player for a lower fee.
Digne, meanwhile, is said to be keen to remain at Barcelona but accepts that he may have to leave as he sits behind Gerard Pique, Samuel Umtiti, Clement Lenglet and Thomas Vermaelen in the pecking order.
Barcelona brought in Digne from Paris Saint-Germain in a £14.9m deal two years ago.