However, the North London outfit have a deadline to do so, with the clause expiring at the end of June next year.
Postecoglou has often opted to use a midfield three featuring James Maddison, Yves Bissouma and Dejan Kulusevski this season, and the results have been mixed so far.
However, during Sunday's 4-1 win against Champions League rivals Aston Villa, the Spurs boss selected a more defensively oriented trio consisting of Rodrigo Bentancur and Pape Sarr alongside Kulusevski, and the Australian manager could look to replicate that set-up going forward.
Journalist Fabrizio Romano reports that Tottenham have the option to buy Real Betis' defensive midfielder Johnny Cardoso for a fee of just £21m, and they will also have matching rights and a percentage on any future sale should they decide not to sign the player.
Cardoso to revamp midfield?
One of the consistent criticisms of Postecoglou's Spurs side since his arrival last season has been the fact that they struggle to keep clean sheets.
Indeed, Tottenham prevented the opposition from scoring on just nine occasions in their last 48 Premier League games, and have kept only three clean sheets in their 21 most recent top-flight matches.
Some have suggested that Tottenham play recklessly, focusing so much on offensive phases of play that it leaves them vulnerable at the back, but Postecoglou has regularly dismissed such notions.
However, providing more cover in the midfield area could enable the likes of Kulusevski and Maddison to maximise their creative potential.
Losing out on Cardoso to a rival could be costly given teams like Liverpool are reportedly still in the market for a defensive midfielder, but at least Spurs have the option to match any offer after the June deadline.
Cardoso compared to Spurs' midfield options
Cardoso ranks quite favourably in defensive metrics compared to midfielders such as Bissouma, Sarr and Bentancur, with the Real Betis player having attempted 13 tackles in La Liga this season, the joint most alongside Sarr.
The American has also made the most blocks of the quartet and has made 10 interceptions this term, with only Bentancur having made more.
Importantly, Cardoso is also comfortable in possession, and he would likely fit into Postecoglou's preferred style of play.
Perhaps pairing the Real Betis midfielder with an energetic ball carrier such as Sarr would get the most out of him, but the American would certainly help give Spurs even more tactical flexibility.