Spurs have dropped into the bottom half of the Premier League table after losing seven of their 15 Premier League games this season.
Their latest setback came at the hands of London rivals Chelsea on Sunday when they lost 4-3 despite going 2-0 up after 11 minutes.
Chairman Daniel Levy is aware Spurs have been hit by injuries to key players and willing to give Postecoglou more time to turn their fortunes around.
The Australian would also like funds in the January transfer window to strengthen the squad.
Spurs have just one win to their name in their past seven matches in all competitions which was their 4-0 thumping of Manchester City.
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Draws have come against Roma and Fulham since then, with defeat at home to Chelsea sealing back-to-back losses.
It came three days after they were beaten 1-0 away at Bournemouth and fan tensions began to boil over at full-time.
Postecoglou was booed when he went towards the travelling supporters, with two stewards standing between him and the crowd.
"They're disappointed and I got some pretty direct feedback, which is always healthy mate," he told talkSPORT afterwards.
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Spurs surrendered a 2-0 lead and lost in a Premier League match for the 11th time in their history on Sunday against Chelsea.
It's the second time they have done so this season, with the first occasions coming away at Brighton when they ultimately lost 3-2.
Postecoglou opted to name Cristian Romero and Mickey van de Ven in his starting XI against Chelsea following their recent absences.
However, Romero was withdrawn after just 15 minutes of play and Van de Ven also went off with an injury later in the match.
Guglielmo Vicario, Richarlison, Wilson Odobert and Mikey Moore are already notable absentees in north London.