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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.