The Portugal international moved to the London Stadium on a short-term deal during the January transfer window after falling out of favour with Luciano Spalletti at San Siro.
The 25-year-old has largely struggled to make an impression on the West Ham hierarchy and the club are still unsure as to whether they will make the move permanent this summer.
But Inter are still desperate to offload the midfielder when the transfer window opens and they have told West Ham that an offer of €28m would be enough to secure his services, according to a report from Calciomercato.
The Irons are yet to express an interest in launching a bid for Mário, who has one goal and one assist to his name for the club. But his parent club are prepared to take a hefty loss on the €40m they paid Sporting CP back in 2016.
Any further talk of potential incomings this summer will likely have to wait until after the season ends, with manager David Moyes having talks over a new contract delayed until it is a mathematical certainty that West Ham will stay in the Premier League next year.
Mário came through the academy at Porto before moving to Lisbon in 2003. The 25-year-old spent 13 years with Sporting CP, including a short-term loan with Vitória Setúbal in 2014, before completing his big money move to San Siro two years ago.