According to the Daily Mail, negotiations over a deal that would see Malcom sign for United next month but return to France on loan for the remainder of the 2017/18 season.
There is, however, a large gap in price at this stage. Bordeaux are said to want in excess of £50m for the player, but United are apparently willing to pay only £33m.
With Jose Mourinho alleged to be keen on Malcom, who cost Bordeaux less than £5m when he arrived from Brazilian club Corinthians in January 2016, talks are therefore likely to continue.
The report from the Mail also claims that the rising star has a 'gentleman's agreement' with Bordeaux that will allow him to leave at the end of the season. There is said to be no release clause.
Malcom has scored seven times in 18 Ligue 1 appearances so far this season, registering a further four assists for his teammates. He is yet to play a senior international appearance for Brazil, but was formally a regular at U20 level in 2015 when he was only 18 years of age.
Malcom helped Corinthians to the notoriously competitive Brasileiro title that same year, playing more than 30 national league games during the season.
United remain linked with numerous attacking players. Christian Pulisic reportedly emerged on the radar last week, while there is now also speculative talk of a summer bid for Paulo Dybala. The one story of interest that seems to have faded, however, is Antoine Griezmann.