The Poland international will leave BVB for Bayern Munich at the end of the season and the Bundesliga giant has earmarked a number of strikers to take his place.
Diego Costa, Jackson Martinez and Adrian Ramos are three of the names on Dortmund's shortlist, but they have now shown an interest in El Shaarawy, too.
The 21-year-old has had a difficult relationship with Milan's board of directors ever since they accepted a 25 million euro offer from Manchester City for the Italy international in the summer of 2013 against his will.
El Shaarawy is therefore open to a summer transfer and a move to the Bundesliga could be a realistic option for the versatile attacker.
The former Genoa and Padova youngster has a contract with Milan until June 2018, but an offer in the region of €20 million could be enough to lure him away from the San Siro side.
El Shaarawy enjoyed a superb 2012-13 campaign, scoring 16 goals in 37 Serie A appearances, but a string of injuries have kept him sidelined for the majority of this season.