Malcom was heavily linked with a move to the Premier League in January but instead decided to stay at Bordeaux until the end of the season, despite reported interest from the likes of Manchester United, Arsenal and Tottenham Hotspur.
A number of previously-interested parties are understood to have since withdrawn from the running, but the 21-year-old could still complete a switch to England this summer.
Sky Sports News reports that Everton have made significant progress in talks for the youngster and are now considered frontrunners for his signature.
Bordeaux's chairman will reportedly meet with representatives of Everton on Thursday to discuss a deal, which could be worth an initial £30m plus add-ons.
The Toffees are thought to be ready to offer Malcom a five-year contract at Goodison Park worth around £80,000 per week.