"I can't see the point of that one," he told the Northern Echo. "Kenwyne is not for sale.
"We have players in the squad who need to go out, but there's no way I want to lose the likes of Kenwyne. He hasn't come to see me. I talked to him the other day and he seemed quite happy."
Tottenham's chances of signing the Trinidad and Tobago international appear to be waning. Only last week Sbragia hit out at the way the club conducted themselves over transfers, accusing them of trying to unsettle players.
Moreover, he insisted that regardless of what they offer, the answer will be no.
"Tottenham seem to be in for everybody and make sure it goes in the papers, which is completely wrong," he said. "What (they) do may unsettle a player and that might be a problem but it's just going to be 'no', it's as simple as that.
"It's wrong to try to unsettle - it's not the way to do business. No matter how many times we say it they keep coming back but as far as I am concerned it was always going to be a 'no' and it always will be a no.
"Kenwyne's an important member of the team and he's hitting form and scoring goals. Sunderland need him. If I'm going to sell my best players I would be better walking out the door."
Meanwhile, Roman Pavlyuchenko has said he is hoping for a rapid return to action after being told the shin injury he picked up against Portsmouth is not as serious as first thought.
The Russian striker is expected to miss his side's Carling Cup semi-final second leg at Burnley tomorrow but could return against Manchester United at the weekend for the FA Cup fourth round.