Though Di Marzio insisted that 'the deal would only take place under certain conditions', the story is unlikely to sit well with West Ham supporters, who will be desperate to see their club keep hold of the forward after he scored 11 goals for the Hammers last season.
Arnautovic spent time on loan at Inter during the 2009/10 season but made just three appearances for the club, with manager Jose Mourinho claiming that the Austrian "is a fantastic person but has the attitude of a child".
Since then, however, Arnautovic has gone on to enjoy great success in the Premier League, becoming a key man at Stoke City during his four years there before joining West Ham last summer in a deal worth around £25m.
This summer has the makings of a busy transfer window for Inter, with the Nerazzurrireportedly already close to completing a deal for Roma's Belgian midfielder Radja Nainggolan.
The club are also interested in turning loan deals for Valencia full back Joao Cancelo and Barcelona midfielder Rafinha into permanent moves, but look set to be priced out of both transfers.
Di Marzio has also reported that Inter could move for Stoke right back Moritz Bauer, an international teammate of Arnautovic with Austria.
The Potters could face a struggle to hang on to their key players following the club's relegation from the Premier League last season, with Serie A and Champions League football likely to prove more enticing for Bauer.