In recent months, Spurs have been plagued by injuries and, as such, have struggled for form, as they sit 14th on the Premier League table after suffering an 11th defeat of the season against Arsenal in midweek.
They have already signed a new goalkeeper this month, with Antonin Kinsky joining from Slavia Prague to ease some of the pressure between the sticks after Guglielmo Vicario suffered a broken ankle.
Spurs are also without first-choice defenders Micky van de Ven and Cristian Romero, as well as winger Wilson Odobert for the long term, and with more issues piling up, Postecoglou insisted he needed reinforcements.
"The club is working as hard as it can and that's all you can ask for," he said. "I do know a lot of work is being done behind the scenes.
"We need reinforcements and need to try and make that happen if we can this week.
"It is trickier in January because you're trying to acquire players from clubs who might want to replace that player, so a lot of logistics involved."
Spurs were rumoured to be in the running to sign Paris Saint-Germain's Randal Kolo Muani on loan in this window, although he is now reportedly closing in on a deal with Juventus.
Asked if his club were in the mix for the France international, Postecoglou said: "It depends what you mean.
"We've been interested in and were looking at a number of players, but did we get to the point we thought he was coming to us? No."
Timo Werner, Brennan Johnson and Yves Bissouma have all added to Spurs' lengthy injury list in the last week. Werner is set for a spell on the sidelines with a hamstring injury, while the latter two sustained issues against Arsenal.
However, Spurs are boosted by a defensive return as Ben Davies, who has missed the last month with a hamstring problem, is in line to return against Everton on Monday (AEDT).
"There's a couple still sore from midweek. Just waiting to see how Brennan Johnson is, he has a bit of a calf complaint," Postecoglou added.