Aston Villa and Celtic are also reportedly interested in the 29-year-old striker.
The Black Cats are ready to pay Spurs £12million for the Republic of Ireland star.
Spurs boss Harry Redknapp has long been considering selling Keane, who faces a heavy fine and is likely to be stripped of the club captaincy after his lead role in an unsanctioned Dublin Christmas party.
Keane re-joined Spurs from Liverpool last January in a £12million deal.
