The South Korea international was forced off with a knock in Thursday's 3-0 Europa League success over Qarabag, although Postecoglou immediately downplayed the severity of his problem after the game.
The Tottenham boss also confirmed on Friday that Son was hoping to train over the weekend, suggesting that there is a strong chance the Spurs captain will be available to sport the armband at Old Trafford.
Son has already created 13 chances from open play this season - more than any other player in the Premier League - and has five direct involvements from his last seven appearances against Man United, four of his own and one assist.
The South Korea international will link arms with Dominic Solanke and Brennan Johnson in the attacking trident if given the all-clear, otherwise Dejan Kulusevski could operate in a more advanced position.
However, the Swede will likely join forces with Rodrigo Bentancur and James Maddison as the midfield triumvirate, while Pedro Porro, Cristian Romero, Micky van de Ven and Destiny Udogie form the first-choice barrier in front of Guglielmo Vicario.
Radu Dragusin's early red card from Thursday night will apply to Spurs' next Europa League game, meaning that he is fine to feature on Sunday, although he will certainly make way for Romero after his Europa League calamity.
Tottenham Hotspur possible starting lineup:
Vicario; Porro, Romero, Van de Ven, Udogie; Kulusevski, Bentancur, Maddison; Johnson, Solanke, Son