“There has been an approach from Barca,” the source confirmed, after Bordeaux had reached an agreement earlier in the day to sell Malcom to Italian giants Roma.
The 21-year-old had been expected to arrive in Rome on Monday night for a medical on Tuesday before joining his future teammates on their pre-season tour of the United States the following day, but had his flight cancelled by the Ligue 1 outfit at the last moment.
Barcelona made contact with Bordeaux following the failure to sign Brazil international Willian from Chelsea and, according to Italian media reports, made a bid larger than the reported fee of 38 million euros ($44.4m) struck with Roma.
Malcom had been a reported target for several European clubs including Premier League sides Arsenal and Tottenham, but English clubs may have been put off from making a bid as he needed a UK work permit to play in the Premier League.
Malcom scored 12 goals in 35 league games for Bordeaux last season.
Roma finished third in Serie A behind champions Juventus and Napoli to qualify for the 2018/19 Champions League group stage, having reached the semi-finals of the competition last term.