The Austrian is on the verge of signing a new four-year contract extension at Stoke after it was rumoured that Everton were not prepared to pay the player £80,000 a week.
The Toffees were supposed to have been keen on Arnautovic given the player's versatility to play across the frontline.
The 27-year-old enjoyed a good campaign for the Potters last season, scoring 11 goals in 34 Premier League games.