According to the Mirror, the 25-year-old Portuguese international enjoyed his time in London and is seeking a return to the Premier League this season.
Having joined the Hammers in January last season on loan, the midfielder made 13 appearances, scoring twice and providing an assist, as West Ham successfully retained their Premier League status.
However, the club failed to make his deal permanent and the player returned to San Siro.
Mario joined Inter in August 2016 from Sporting CP, in a move that cost the Serie A side £35m. He has since made 44 league appearances for the club, netting three times.
Mario is a senior Portuguese international, making his full debut back in October 2014 against France, and has 40 caps to his name. He has scored two senior international goals.
The 25-year-old was part of Portugal's World Cup campaign this summer in Russia, playing four games for his country.
He has found himself generating significant interest, with Spurs one of the front runners as chairman Daniel Levy looks to make up for a current transfer drought. Tottenham are the only Premier League club yet to make a signing this summer.
Levy is considering the late loan move for Mario as a way to bolster manager Mauricio Pochettino's squad, having grown frustrated and impatient over a deal for Aston Villa's Jack Grealish.
The north London club have offered £25m for the midfielder but were reportedly stunned to learn Villa want over £30m before they will be prepared to allow Grealish to leave.