Spurs rekindled their interest in Damiao towards the latter stages of the transfer window after it emerged Jermain Defoe was struggling with a pelvic injury.
With his other only recognised hitman Emmanuel Adebayor away at the African Nations Cup, manager Andre Villas-Boas was thought to be interested in adding another striker to his squad.
Tottenham reopened negotiations with Internacional over the potential transfer of long-term target Damiao, but the Brazilian club do not want to sell the 23-year-old, who was top scorer at last year's Olympics, and Press Association Sport understands no deal will be struck before the transfer deadline.
Spurs have a partnership with the club, however, and they could return with a fresh bid for the star this summer.
Most of the attention around the north London outfit has been concerned with outgoings on Thursday. Heurelho Gomes has joined Hoffenheim, while Jermaine Jenas, David Bentley and Andros Townsend are in talks with QPR.
Lewis Holtby and Zeki Fryers have been the only two arrivals at White Hart Lane this month, but given Spurs' history of late activity in the transfer market, chairman Daniel Levy could make one last swoop before the window shuts.
Internacional director Marcelo Medeiros later claimed Tottenham's attempt to sign Damiao failed because they did not offer enough money for the Brazil international.
"Leandro Damiao won't leave, the offer was below what we wanted," he was quoted as saying on Globo Esporte.