According to Spanish outlet Fichajes, the North London club have made a bid of €45 million (£37.6m) in order to beat rivals to the signing of Rigg, 17.
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Ange Postecoglu’s side are said to be ‘determined’ to beat the likes of Man United and West Ham to the signing.
Tottenham pulled off a similar move last summer, signing highly-rated midfielder Archie Gray from Leeds United.
Rigg has been a key player for Sunderland as they push for promotion back to the Premier League, scoring four goals and providing one assist in his 36 games.