Tottenham have once again been linked with Chelsea midfielder Conor Gallagher, as the England international is still yet to sign a new deal at Stamford Bridge.
But Spurs, who host Brentford on Wednesday night, are running out of time and Postecoglou admitted it is “unlikely” that the club completes any more business before the deadline.
“I don’t see any incomings,” Postecoglou said. “Outgoings might be a little bit different, because I’m not totally engaged with that, and other people are doing the work around that. I’d say unlikely on both fronts, without ruling anything out.”
Postecoglou has been working alongside Tottenham’s new technical director Johan Lange on transfers this month and the Australian said he had “less involvement” in discussions than he did in the summer.
“It’s been a bit different,” Postecoglou said. “With Johan and his group of people working alongside him, I’ve had less involvement in a lot of the preliminary stuff. My role stays specific to probably what it should be, around the final decision."
Tottenham only have the Premier League to focus on over the second half of the season after Friday’s defeat to Manchester City in the FA Cup fourth round, but they are still in the hunt for a top-four finish.
"It’s disappointing that we’re out of both cups and not being in Europe because our supporters are really crying out for success,” Postecoglou said.
"I can’t let that guide my course, we’re still growing as a team and finishing the second half of the year stronger than the first will put us in a good position to continue to challenge.
"It’s not just about winning one trophy. If we want to compete at that level, there’s still a lot of work to do."
Spurs are set to welcome back key midfielder Pape Matar Sarr on Saturday following Senegal’s exit from the Africa Cup of Nations on Monday night.