The Reds striker is surplus to requirements at United after making just 76 starts in four and a half seasons.
Black Cats boss Keane, who knows the France international's qualities well after starring alongside him, could wipe the slate clean and give the troubled player a fresh start.
Keane believes that a change of scenery will benefit Saha and re-start a career which bristled with promise when he joined the Reds from Fulham for £12.8m in 2004.
Saha's fate as a United player is expected to be sealed if the Reds, as seems likely, land Dimitar Berbatov from Spurs before the new season kicks-off.
But for now, Sir Alex Ferguson and his squad fly to South Africa tomorrow afternoon unsure of the final make-up of the squad for next season.
As the Reds gear up for the new term with a friendly against Kaizer Chiefs on Saturday, the United boss is awaiting progress in the Berbatov chase.
Spurs are holding out for more than the £20m United are initially prepared to spend on the Bulgarian goalscorer.
United have previous experience of protracted transfer dealings with Tottenham when Michael Carrick signed in 2006 after a saga of several weeks.
Should United sell Saha, and for how much? Have your say.
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Octavius Tinsworth Ace (16/07/2008 at 09:24)