The 30-year-old recently returned to the Liberty Stadium following a loan spell with Leeds United and has two-and-a-half years remaining on his Swansea contract.
"I have come back feeling fit and I am just trying to get back into the squad and into the team," Tate told The Sentinel.
"Obviously the team have been doing very well so it's going to be hard to get back in, but at the end of the day I am not a quitter so I will be here giving it a go.
"This is my club. This is where I want to be."
Tate has made four appearances for Swansea this season.