The 29-year-old missed most of last season with a broken leg after a golf buggy accident.
There had been reports that the defender wanted a fresh start, with the Swans having appointed a new manager in Michael Laudrup over the summer.
The former Manchester United trainee is aware of the reports and says that nothing could be further from the truth.
"I was only out of the side when I was injured," said Tate. "But that is part and parcel of the game.
"The injury was unfortunate but, as I say, I am not a quitter so I will get my head down and put in a lot of hard work.
"My future is here because this is my club. I am not going anywhere and I have never thought about going anywhere."
Tate, who played as Swansea defeated Barnsley 3-1 to progress to the third round of the League Cup, could be in contention when the Swans face Sunderland on Saturday.