Malcom has an €180m (£160m/$200m) termination clause in his current contract with the Liga champions, but Barca would accept his departure in exchange for €1m more than the €41m they spent to sign him from Ligue 1 side Bordeaux.
But after a bright 2017-18 season with Bordeaux in which he scored 12 goals and added seven assists, Malcom struggled for playing time at Barca, managing 15 appearances for the club and just six starts in La Liga.
Without opportunities during the 2018-2019 season, Malcom was a serious candidate to leave Barca this summer.
However, there had been a lack of significant offers for the 22-year-old, with just a slight interest from Arsenal in a possible loan, which kept him involved in Barca’s pre-season plans.
But the situation looks set to change with Dortmund, who have already brought in a pair of attacking players in Thorgan Hazard and Julian Brandt this summer, now involved.
The 2018-19 Bundesliga runners-up enjoy good relations with Barca after the successful move of striker Paco Alcacer to Dortmund last season.
Alcacer enjoyed a breakout campaign in the Bundesliga, with the 25-year-old Spain international scoring 18 goals to finish second in the Golden Boot race behind Robert Lewandowski.
But, while talks are ongoing between Barca and Dortmund, if a deal is to be done for Malcom it will not be official until next week, when it is expected the Catalan club will have more transfers, both inbound and outbound, agreed.
Malcom is currently in Japan along with the rest of the Barca squad for their pre-season Japanese tour and plans to return to Catalunya next Sunday after the game against Vissel Kobe the day before.