The Cote d'Ivoire international would be open to a move to last season's Champions League finalists as they are looking for a new striker
The Poland international will leave BVB for Bayern Munich at the end of the season on a Bosman transfer and Dortmund are keeping tabs on a number of players to take Lewandowski's place.
They have previously been linked with high-profile names such as Diego Costa and Jackson Martinez, and the 26-year-old Doumbia now appears to be a candidate, too.
"Seydou has heard about Dortmund's interest and is happy about it," the striker's representative told Sport Bild.
"If he were to leave CSKA Moscow, it would only be for one of the biggest clubs in the world. Borussia Dortmund are definitely among the top teams.
"We are happy to open talks if they make an approach."
Doumbia has a contract with CSKA until June 2015.