The Potteries are holding out for £20m for the Austrian winger and have know seen off two West Ham approaches for the wantaway striker, with City holding out for £20m.
The Hammers have already had a £15m bid for Arnautovic rejected by Stoke, with manager Mark Hughes not wanting to sell but chairman Peter Coates saying a deal can be done at the right price.
Stoke are aiming for a £17m profit on the player they signed from Werder Bremen for just £3m back in 2013 and who has been a big hit at the Bet365 Stadium.
Arnautovic handed in a transfer request at Stoke after learning the £15m bid was rejected for his services from the Hammers, with his agent and brother trying to force through a move to east London.
It’s not yet known for sure if the Hammers will go back in with another bid for the 28-year-old but Slaven Bilic is very keen to sign him along with Javier Hernandez.