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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.