Keane enjoyed two spells at White Hart Lane totalling eight years before moving to the Los Angeles Galaxy two years ago.
The Republic of Ireland striker will train at Spurs' Enfield base to maintain his fitness ahead of the start of the MLS season in March.
Keane spent the last American off-season on loan at Aston Villa, but even though Spurs are down to only one striker with Emmanuel Adebayor at the African Nations Cup, manager Andre Villas-Boas is not thought to want to sign the 32-year-old on a temporary basis.
Keane himself ruled out a loan move back to England two weeks ago, admitting he needed a rest following a tiring 2012 with the Galaxy and the Republic of Ireland.
"It's been a long season, with the Euros and what have you. I've a few little niggles that need to be sorted out so I don't think at this moment in time it would be right for me to go anywhere," he told Sky Sports.