The Spurs have already brought in Radu Dragusin and Timo Werner, but had eyed other targets to boost their chances of Champions League qualification.
The north London club had been linked with a moves for Chelsea midfielder Conor Gallagher and Club Brugge winger Antonio Nusa.
But with 24 hours left in the window, Postecoglou has closed the blinds on any potential incomings in what has been a quiet month for Premier League sides.
"Unlikely I'd say," said the Australian head coach when pressed on Spurs' hopes of bring adding to their squad.
"I don't see any incoming. Outgoings are a little bit different because I'm not as engaged on that. Others are dealing with that but I'd say also unlikely."
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Postecoglou is preparing his side for Wednesday night's visit of Brentford in a crucial clash in the race for the top four.
Spurs are currently fifth, three-points adrift of Aston Villa, with all to play for in the coming months.
Postecoglou's men are showing signs of finding their feet again after a wretched November that saw them lose top spot after collecting just one point from a possible 15.
Tottenham drew 2-2 at Manchester United in the last Premier League fixture and a return to winning ways against Brentford would provide the perfect opportunity to kickstart their quest for a return to European football.
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The Spurs boss confirmed that despite his exit in the Africa Cup of Nations with Senegal, Pape Matar Sarr will miss Wednesday's game but could be in contention for a return in Saturday's trip to Everton.
"The latest I heard is he should be back tomorrow at some stage," Postecoglou added. "Disappointed for him and Senegal. From our side he's a key member of the squad, we'll have him back and he should be available for Saturday."
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Meanwhile, Manor Solomon, Giovani Lo Celso and Ryan Sessegnon will all miss the London derby with Brentford through injury.