Former Wigan striker says he wants to stay with Werder Bremen.
Sunderland's sporting director Lee Congleton worked with Di Santo at Chelsea, where Di Santo spent a season in 2009/10.
The 26-year-old has only one year remaining on his current deal, but has his eyes on an extension.
He told BILD: "Many wanted me, but I have already said, I will prefer to stay at Werder. We are in talks together. I would like to extend, and I hope Werder sees it that way."
Di Santo struggled to score regularly at Wigan Athletic, netting only 13 times in 97 games. His spell at Werder Bremen has been more productive.
The attacker has scored 18 goals in 51 games for the Bundesliga side, and was a regular for them last season.
His decision to stay put may not be a negative for Sunderland. Two seasons ago they signed Jozy Altidore, a player who struggled at Hull, but scored regularly for AZ in Holland.
Once he returned to the Premier League, he flopped, back to his old Hull form, and Di Santo is a repeat waiting to happen.