Al-Habsi is on the books of Wigan Athletic at the moment, but his current contract with the Latics runs out at the end of the month after which he will become a free agent.
While Spurs are looking to replace Brad Friedel, London rivals West Ham want someone to take the place of Jussi Jaaskelainen in the squad.
Championship club Reading are also reported to be monitoring Al-Habsi and want the Oman international to replace the Bournemouth-bound Adam Federici.
Which club should Ali Al-Habsi join?
Moving to Tottenham would see Al-Habsi play for one of the biggest clubs of England and also have the chance to feature in Europe.
However, the 33-year-old will be the third-choice goalkeeper at Spurs behind Hugo Lloris and Michel Vorm, and he is unlikely to get much playing time.
Al-Habsi would face a similar situation at West Ham, where Adrian is the undisputed number one between the sticks and Darren Randolph has been signed on a free transfer as his back-up.
Moving to Reading, though, will allow Al-Habsi a better chance of playing regular first-team football, but he will be turning out for a team who are unlikely to push for promotion.