The 23-year-old Brazil international has been linked with a move to Tottenham for the past few transfer windows, but the report claims Borussia Dortmund have identified Damiao as a potential replacement for Robert Lewandowski.
The Polish striker has been linked with a move to Manchester United, and according to German newspaper Bild, the reigning German champions are believed to be preparing for his exit.
Tottenham reportedly made a last-minute deadline day bid for Damiao in the January transfer window, and the north London club were thought to be interested last summer when the Brazilian was taking part in the Olympics.
Andre Villas-Boas has just two senior strikers - Jermain Defoe and Emmanuel Adebayor - and the Spurs manager is believed to be keen to bring in another at the end of the season.
Tottenham are pushing to secure a Champions League qualification spot, and they'd be expected to enter the market should they qualify for next year's competition.
They currently sit third in the Premier League table, five points behind Manchester City and seven points clear of fifth-placed Arsenal.
The report also claims Champions League chasing Napoli are also in the hunt for Damiao, and could move for the Brazilian depending on the future of their own South American goalscorer, Edinson Cavani.