Spurs skipper Son in race to recover from injury for Man Utd clash
Son limped off with a hamstring injury in the 71st minute of Thursday's 3-0 win against Qarabag in the Europa League.
Postecoglou was uncertain about the extent of his captain's injury immediately after the Qarabag tie.
But he said on Friday that the South Korea forward wants to train on Saturday to show he is ready to feature in the Premier League showdown at Old Trafford.
"Fair to say the boys are fairly tired, the ones who put in a shift. Apart from Sonny, everybody is okay," Postecoglou told reporters.
"Sonny, I don't think is too bad. He wants to train tomorrow and we will see how it goes and make a decision from there. We have another day up our sleeve to give him every chance."
If Son is unable to recover in time, Postecoglou has several options on the left wing, including Sweden international Dejan Kulusevski.
Germany's Timo Werner replaced Son on Thursday, while 17-year-old attacker Mikey Moore could be handed a full debut.
"Timo and Mikey can certainly come into the frame. We have Kulusevski who can play wide as well so we've got some options there, but firstly we'll see how Sonny is," Postecoglou said.
Son's long-term future in north London was thrown into the spotlight earlier this week after he said no talks over a new contract had taken place with the Tottenham hierarchy.
Son's current deal expires next year but Tottenham hold the option to extend his contract by a further year and reportedly plan to activate that clause.
Postecoglou made it clear he wants the 32-year-old to stay, with Son into his 10th season at the club he joined from Bayer Leverkusen in 2015.
"I don't always have the final say but certainly I like to think my input is significant on it," he said.
"I think it is part of a broader discussion around Sonny but the way he is performing and leading the club at the moment, I certainly want him to stick around for a while."
