The 17-year-old has impressed for the Black Cats, who are chasing promotion from the Championship.
Spurs are among a number of clubs to have been linked with him this season amid speculation over his long-term future.
Tottenham have a policy of buying promising youngsters – their big-money signing of Archie Gray from Leeds being a prime example.
And Spanish transfer-gossip website Fichajes have claimed that Spurs have now lodged a bid in an attempt to take Rigg to north London and add him to boss Ange Postecoglou’s squad this summer.
Rigg has made 36 appearances for Sunderland in all competitions so far this season, scoring four goals.
He has previously made it clear that he is happy at the club.
“I think some people don’t realise how much it means to put on a Sunderland shirt and give it your all for the team,” he said in an interview with the club’s media team, as reported by the Sunderland Echo.
“ I think I can say that I do every time I go on the pitch. So yeah, it’s very special for me to be playing, and I’m trying to take every opportunity that comes. Yeah, I think that probably sums it up, to be honest.”
