It comes after the North London club lost 2-1 at home to English Premier League strugglers Leicester City on Sunday afternoon.
It was Spurs' third defeat in four games, but according to football.london, the club will keep Postecoglou in charge for now.
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The hierarchy are said to understand that the squad is ravaged by injury, so they will try to sign one more player before the January transfer window shuts next week to ease Postecoglou's worries.
The Australian, though, currently has the club flirting with relegation. Spurs are 15th in the English top flight and only eight points above the drop zone.
Yesterday's loss saw tensions spill over among supporters at full-time, with one fan telling Postceoglou the club will 'go down' with him at the helm.
Spurs face Elfsborg in the UEFA Europa League on Thursday evening as they aim to bounce back from another disappointing defeat.