The 31-year-old striker admitted earlier this week that he expects to leave White Hart Lane after spending much of last season on loan at West Ham, where he scored just two goals.
LA Galaxy are thought to be a possible destination, where Keane could link up with David Beckham.
"We are always looking to improve our squad and have contacted or been contacted by a host of players during the current transfer window," said an LA Galaxy spokesman.
"As soon as we have something confirmed in regards to any potential player acquisitions we will be sure to alert everyone."
Blackburn, Bolton and Leicester are also believed to be interested in the Republic of Ireland international.