The former Watford and Manchester United man was understood to have been considered for a short-term move to North London due to Hugo Lloris's serious knee injury.
Lloris sustained damaged ligaments during Spurs' victory over Manchester City earlier this month, and the Frenchman is set for five to seven weeks on the sidelines.
Tottenham are hopeful that Lloris will not need to undergo surgery and can return for the second half of the season, but Antonio Conte has been left short of experienced goalkeeping options.
Backup shot-stopper Fraser Forster has stepped in for Spurs' recent defeats to Leicester City and AC Milan, while Brandon Austin and Alfie Whiteman are also in reserve.
However, Austin is yet to make his senior competitive debut for Tottenham, while Whiteman's only appearance came as a substitute in a Europa League win over Ludogorets in November 2020.
As a result, Tottenham were supposedly hoping to add to their goalkeeping ranks by bringing in Foster, who retired after running down his contract with Watford at the end of last season.
Teams need special dispensation to register emergency signings outside of the transfer window, though, and the Daily Mail claims that Tottenham have been blocked in their efforts to sign Foster.
The 39-year-old was presented with the chance to join Newcastle United after ending his stint at Watford, but he ultimately turned down the role of Nick Pope's understudy.
Foster, who now runs a successful podcast, revealed that he rejected the chance to join the Magpies largely due to family reasons, and it is unclear if he would have been open to coming out of retirement to join Spurs.
During a career spanning over two decades, Forster kept 94 clean sheets in 390 Premier League appearances, while also earning eight caps for the England national team.
The 39-year-old won two Premier League titles and two EFL Cups with Manchester United, as well as another EFL Cup crown with Birmingham City in the 2010-11 campaign.
Lloris is being kept company in the Tottenham treatment room by both Rodrigo Bentancur and Yves Bissouma, the former of whom is out for the rest of the season with an ACL rupture sustained in the weekend's Premier League loss to Leicester City.
Meanwhile, Bissouma could also sit out the remainder of the campaign due to a stress fracture in his ankle, which he has gone under the knife for, while Pierre-Emile Hojbjerg was unavailable for Tuesday's Champions League clash with AC Milan through suspension.
As a result, Pape Sarr and Oliver Skipp paired up in the engine room at San Siro, earning praise from Conte and Tottenham talisman Harry Kane, who hailed the pair's "outstanding" displays.