Spurs have long been linked with a move for Damiao, and failed with a January deadline day deal for the Internacional forward.
Although Tottenham boss Andre Villas-Boas insists he has no plans to reignite the move in the summer, reports suggest the Portuguese boss may be bluffing and that the north London club are still keen on getting the deal done.
That may be a little more complicated now after TalkSport claimed that Napoli are in the hunt for the 23-year-old's signature.
According to the radio station's website, the Serie A outfit will look to lure Damiao to Naples if they lose Edinson Cavani over the summer.
Cavani, who has a release-clause of €63 million written into his contract, has been linked with a move to Chelsea and Manchester City, but now appears close to sealing a switch to Real Madrid.
Spurs are unlikely to able to match Napoli's financial muscle if they are able to lure Damiao to Italy using the cash generated by Cavani's transfer.