The 21-year-old was heavily linked with a move to the Premier League in January, with the likes of Manchester United, Liverpool and Arsenal all credited with an interest.
Bordeaux managed to hang on to Malcom until the end of the 2017-18 season and, this summer, Spurs emerged as the English club rumoured to be most interested in the Brazil international.
According to Tuttomercatoweb, however, Inter's offer is the only one close to the Ligue 1 club's £45m valuation for their asset.
The report claims that the Italian club have offered £8.8m for an initial loan and the option to purchase the player on a permanent deal for a further £26.5m next summer.
Malcom scored 12 goals and grabbed seven assists in 35 league appearances last season.