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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.