The 16 year-old wing-back is a target for Borussia Dortmund and Bayer Leverkusen, says The Sun.
And it's suggested the England U17 captain could be willing to depart this summer.
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Manchester United have been watching Rigg, who rejected an offer from Newcastle before signing pro terms with the Black Cats.
Rigg is the youngest Sunderland debutant at 15 and also their youngest goalscorer.