Inter have offered €40 million (£35m/$47m) to secure his services, but Bordeaux are holding out for closer to €50m (£43.8m/$58.7m).
Malcom has become one of Europe's hottest properties having scored 12 goals and laid on a further seven assists for Bordeaux during the 2017-18 Ligue 1 campaign.
Arsenal looked to bring him to the Emirates Stadium in January as a potential replacement for the departing Alexis Sanchez while Tottenham have long been credited with interest.
Bayern Munich have also been heavily linked with his signature while the player himself has previously spoken of his dream to play for Paris Saint-Germain.
Inter, though, have now moved into pole position in the race for the former Corinthians starlet as they prepare for their return to Champions League football.
The Nerazzuri will play in Europe's premier club competition for the first time since 2011-12 having finished fourth in Serie A, and have already begun bolstering their squad by agreeing a deal for Lazio defender Stefan De Vrij.