Postecoglou not expecting Tottenham to make any signings in final days of transfer window
Fifth-placed Tottenham have brought in forward Timo Werner on loan from RB Leipzig and signed defender Radu Dragusin from Genoa this month, as they look to break back into the top four.
"Unlikely, I'd say. I don't see any incomings," Postecoglou told reporters in London.
But Spurs will welcome back midfielder Pape Matar Sarr, who started 16 league games this season before leaving for national duty with Senegal at the African Cup of Nations, where they were knocked out in the second round.
"He should be back tomorrow at some stage. Disappointed for him. Senegal kind of had a real ambition to win the competition... He should be fine for Saturday," Postecoglou said.
The manager praised Brentford and England striker Ivan Toney, who scored 19 minutes into his comeback earlier this month from an eight-month ban for betting offences.
"As soon as he comes into that team he gives them a different look," he said. "So much of (Brentford's) attacking threat revolves around him."
Tottenham trail fourth-placed Aston Villa by three points, and were knocked out of the FA Cup after a fifth-round loss to Manchester City on Saturday.
"I think the other night gives us a sense of where we are at a little bit with regards to our destination. But in terms of our starting point, I really believe we have made progress... the results are slowly inching our way as well," he said.
"If we continue to make progress... there's belief in us that we can bridge that gap at some point."
Postecoglou also said Liverpool manager Jurgen Klopp's decision to leave the club at the end of the season came as a "shock to everyone."
"It is hard these days to stay at one club for a long time... when you stay at one club and you need to do one, two, maybe a third rebuild, it can be taxing. He's done it, he's an unbelievable manager," he said.
"I'm interested to see how long his sabbatical lasts. I'm kind of hoping it lasts for a while because it gives me hope... because I have those thoughts in my mind often.
"I've got a sense it just drags us back in, but I hope he does have the break that I think he deserves."
