The 21-year-old winger was linked with a move to Fulham's London rivals Arsenal and Tottenham as well as German giants Bayern Munich during the January transfer window, but the Sun report the Cottagers are set to continue their ambitious spending by making Malcolm their third summer signing.
Manager Slavisa Jokanovic has already added Nice midfielder Jean-Michel Seri, who nearly joined Barcelona last year, to Fulham's ranks this summer, and the Ivorian has signed a £100,000-a-week contract at Craven Cottage.
And Fulham, who will appear in the Premier League for the first time since 2014 following their promotion from the Championship, are hoping to secure another major coup by acquiring Malcolm's services before the start of the season.
However, the Cottagers will need to act quickly as Serie A side Inter have already tabled a bid to Bordeaux for the 21-year-old winger.
I Nerazzuri have offered the Ligue 1 side a £8.8m season-long loan move with an option to buy for a further £26.5m once the temporary deal expires, according to the Sun's Warren Houghton.
Yet the French club value the Brazilian at £45m, and will be prepared to do business with Fulham should the west London club meet their demands.
Malcolm joined Bordeaux from Brazilian side Corinthians in 2015 for an undisclosed fee and has made 80 league appearances for Les Girondins, scoring 20 goals. The 21-year-old was his club's top goalscorer last season, finding the net 12 times in 35 league appearances.
The winger also represented his native Brazil at the 2016 Olympic Games in Rio de Janeiro, but has yet to be called up to the men's senior team.