Everton appointed Ronald Koeman as their new manager earlier today.
The Austrian international has stalled over signing a new contract at the Britannia Stadium, and new Everton boss Ronald Koeman is believed to have made him one of the Toffees’ main transfer targets this summer.
Arnautovic only has a year left on his deal at Stoke, meaning that Mark Hughes’ side may be forced to sell unless he signs new terms.
The Potters are determined not to lose Arnautovic on the cheap, but they realise they could be powerless to resist if Everton offer them a serious amount of money.
According to The Sun, a bid of around £13 million would be deemed acceptable by Stoke.
Arnautovic scored 12 Premier League goals for Stoke last season, and was one of the Potters' main attacking threats.
Whether Everton will be willing to pay a big fee for Arnautovic remains to be seen, but it is believed that the Merseyside club have plenty of funds to spend this summer.
Everton have reportedly handed Koeman a £100 million transfer budget, as they look to strengthen their squad for next season.