The 29-year-old has been a revelation at the London Stadium since he arrived at the club before the start of last season, becoming a talismanic figure in east London after then manager David Moyes chose to utilise Arnautovic as a lone striker.
He knows the West Ham fans love him and he has a special connection with them, but things move on, this is the world of sport, and he hopes they can understand.
It was believed that West Ham were ready to offer the Catalans giants £20 million for the services of the Spain worldwide, but a source inside the London Stadium poured scorn on that notion.
Pellegrini underlined his determination to keep Arnautovic before West Ham's meeting with Arsenal on Saturday, with the club later issuing a statement which read: "Marko has a contract and we fully expect him to honour it".
Pellegrini added that the two-time Premier League winner's previous experience sets him in good stead for his return to football with West Ham. Until he is no longer a West Ham player, he will give everything to the club.
West Ham bought Marko for peanuts. He wants to go to a new market and challenge for titles.
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"Players of his quality and other players like Declan Rice, Felipe Anderson, other clubs will want them but that is one thing".
"I'm looking forward to the next game, a derby against Arsenal so I'm sure the atmosphere will be even more insane".
Since arriving from Stoke City in summer 2017, Arnautovic has established himself as a key player at West Ham.
Manager Manuel Pellegrini had earlier said he was determined to keep Arnautovic, who has scored eight goals this season, including three in his last two matches. I don't think they will go.
"Marko and the other players involved in the rumours have their heads here, they want to continue the way they're playing". At the moment it's all so slow and predictable and the whole game is being played in a 30-yard space.
According to the Daily Star, as cited on HITC, the Hammers could launch a January move to sign the Belgian, with Perez attracting interest from elsewhere. Although after Payet you never know what's round the corner.