Reports emerged last week suggesting that new Spurs boss Mauricio Pochettino was keen to recruit the 33-year-old - who joined Sunderland from Manchester United in 2011.
However, speaking back in his native Ireland, O'Shea has played down talk of a move.
"It was news to myself," O'Shea told the Irish Daily Mirror.
"That’s the way it goes at this time of the year, there is lots of stuff rumoured about players coming and going.
"It’s just one of those things. It’s just total speculation.
"I’m in the game long enough to know that and I’m more than happy with Sunderland."
O'Shea has played over 100 games in his three seasons with Sunderland and insists he is looking to continue turning out at the top level for a while longer.
"I definitely want to play on beyond next season," he said.
"I played around 50 games last season and I'm fit and well, and long may that continue.
"I'm already looking forward to next season after what was a roller-coaster end to last year.
"But as for my future, that will be down to Sunderland.
"I've never forced the issue throughout my career and I’m not about to start now.
"Look, it was great getting to the League Cup final and that was definitely an ambition when I joined Sunderland, to get to a Cup final and obviously to win one.
"It would have been special had we held on that day but unfortunately that brilliant Yaya Toure goal put City back in it before Samir Nasri won it."