The 30-year-old defender made the switch to Elland Road from Swansea last month and has become a regular fixture in Neil Warnock's side.
Tate has played a part in three victories since his arrival and Warnock has made no secret of his desire to hold on to him beyond January.
"Three wins in four games is a reasonable return so you've got to be happy with that," Tate told the club's official website.
"I think I've done pretty well so far. Even though we got beat on Saturday, I thought I did okay, and it's one of those things where I'm only going to get stronger.
"I haven't spoken to anyone about it (beyond the end of the loan). I can't say what's going to happen.
"I'm loving it at the minute though. Elland Road is a great place to play. We've had two home games and I'm looking forward to Saturday. Leeds is a great city and it's a great place to live."
- Sports & Recreation
- Neil Warnock