Tottenham to make late call on captain Son for Manchester United clash
Son looked in discomfort in the second half of their 3-0 home win over Qarabag on Thursday and was taken off after receiving treatment, with Postecoglou saying after the game that the forward was fatigued.
He has been a key player for Spurs early in the season with two goals and two assists, and Postecoglou said they will assess him ahead of Sunday's trip to Old Trafford.
"It's still early days from last night. Fair to say the boys that put in a shift are fairly tired," Postecoglou said.
"Apart from Sonny, everyone's ok, but I don't think it's too bad (with Son). He wants to train tomorrow so we'll see how he goes at training and make a decision from there. We have another day up our sleeve to give him every chance."
Son is in the final year of his contract and Postecoglou said he wants the South Korean forward, who joined the club in 2015, to extend his stay with the north London side with whom he has scored 164 goals.
"I don't have the final say but my input is significant. The way he's performing and leading the club I want him to stick around for a while," the manager said.
Spurs held United to a draw at Old Trafford last season and Postecoglou said he was looking forward to playing there again, adding there was no fear factor of playing at the iconic stadium.
"I've never been scared of a venue... What makes venues unique is the atmosphere and when we played there last year it was brilliant," he said.
"The supporters got behind their club - I'm not sure if that's changed. It's a great stadium with the history and tradition behind it. It's a game players and managers get excited about."
His United counterpart Erik ten Hag has been under pressure to deliver results but Postecoglou said the Dutchman had done a "great job" despite the criticism.
"He keeps mentioning he's won two trophies and that's not insignificant. Everyone keeps saying that is all I need to do but then there is always something expected after. It is a difficult job," he said.
"It is tough to go to Old Trafford. Irrespective of managers, it is still a rather compelling home record. It is one we will be ready for."