They are also in contention to qualify for the next stage of the Europa League, and will play Tamworth in the third round of the FA Cup on January 12.
Postecoglou added, “It does not seem that our agenda will ease at any stage. So I think it makes sense. We will try to strengthen our ranks.”
“You don't want to just panic and bring in anyone that you don't think is going to help our cause in the last half of the year, but I think we've already shown that we're very methodical and careful in our work.”
Postecoglou has faced questions about Tottenham's recent Premier League results and tactics, but refused to blame his players.
He added: “They are giving the absolute maximum effort and that is supported by the physical standards you set for what they do. They are trying to do it the way I ask them to do it. How can I be?” Criticize that?
Postecoglou also defended his reaction last week, where he accused a Match of the Day reporter of downplaying the impact of Tottenham's defensive injuries following their defeat by Liverpool.
“I wasn't angry, but I don't know many managers who give interviews after a defeat and are all cheerful,” he said.
“It's fair to say I'm tired of the same questions over and over again, and maybe after a defeat it's easier to get a reaction.”