Sky Sports reports that the 34-year-old is in ‘advanced talks’ with the Black Cats.
The former Manchester United striker is a free agent after leaving Tottenham at the end of the season.
Saha could be signed by Sunderland ahead of the season opener with Arsenal at the weekend.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.