Postecoglou has been one of the more active Premier League managers during a slow January window.
The Australian brought Romanian defender Radu Dragusin and German forward Timo Werner to north London.
Tottenham have also been linked with Chelsea midfielder Conor Gallagher and Club Brugge winger Antonio Nusa.
But Postecoglou said his club's business is probably done ahead of Thursday's deadline.
"Look, unlikely I'd say. I don't see any incomings," he said ahead of Wednesday's Premier League game against Brentford.
"Outgoings, a little bit different because I'm not totally engaged with that. Other people are doing the work around that.
"I'd say unlikely on both fronts, without ruling anything out.
"I've enjoyed working with (technical director) Johan (Lange) and his team. I am sure going into the summer we'll be in a good place to make sure we again try to take advantage of the fact we can make our squad and team stronger for what is ahead."
Tottenham will aim to bounce back against Brentford after their FA Cup fourth round exit against Manchester City on Friday.
It means the club's trophy drought is set to extend into a 17th year unless they can win the title this season.
"It's disappointing we're out of both cup competitions, particularly with not being in Europe because obviously the supporters are really crying out for some sort of success to experience at this football club, but I can't let that guide my course," Postecoglou said.
"This is still about us growing as a team and finishing the second half of the season stronger than the first.
"If we do that, we'll be in a good position to continue to challenge and push this team along. That's our focus.
"As much as there's disappointment that we're out of another cup, there's also a reminder to us that it's not just about winning one trophy. If we're going to compete at that level we want to, then we've still got a lot of work to do."
