Terra says Atletico will seek to close the Germany international's transfer after Friday's Super Cup second-leg clash with Real Madrid.
Reus, it is expected, would sign on Saturday and be in Madrid on Monday for his presentation ceremony at the Vicente Calderon.
Atletico will seek to agree terms over a €25 million fee with BVB, plus a further €5 million due in bonuses. Atletico would also grant first option to BVB for several of their young players, including Oliver Torres, who is admired by Dortmund coach Jurgen Klopp.
Reus' deal carries a €45 million buyout clause, but with less than 12 months to run, BVB know they need to sell now.
For the big stories and the banter follow us on Twitter: @tribalfootball