Spurs have been without James Maddison since November
Midfielder Maddison has been absent since November with an ankle issue.
Tottenham defenders Micky van de Ven and Cristian Romero are fit, while City striker Erling Haaland is close to returning but is not yet available.
Spurs host City in the fourth-round tie at Tottenham Hotspur Stadium (20:00 GMT).
Postecoglou said of Maddison that "there aren't too many in the league that are like him".
He added: "It just helps our ability to prepare for the challenges ahead. We have been through a difficult period."
Haaland, who is level with Liverpool's Mohamed Salah at the top of the Premier League scoring standings with 14 goals this season, has not featured for City since early December with a foot injury.
"[He is] still not ready for tomorrow but he is close," said City manager Pep Guardiola on Thursday. "He trained, is not perfect and we will wait a little bit more."
Switzerland defender Manuel Akanji is still out for City, but defender John Stones and goalkeeper Ederson are available for selection.
-- Courtesy of BBC Sport