Son was involved with South Korea at the Asian Cup where they lost to Jordan in the semi-final on Tuesday while Bissouma's Mali exited the Africa Cup of Nations last weekend at the quarter-final stage.
Spurs, fifth in the standings on 44 points, host Brighton on Saturday, with Roberto De Zerbi's side in eighth place on 35 points.
"Sonny and Biss they trained well. Sonny did recovery on Thursday and trained today," Postecoglou told a press conference.
"He is very disappointed for Korea's exit, at the semi-final stage you feel so close. But he gave everything for his nation, no-one could question his commitment.
"I spoke to him after and he was keen to be back, so no surprise he was back training straight away."
The manager also played down concerns over Bissouma, after media reports that he had played through the illness with malaria at the tournament.
"No, that's not right. He had a slight form of malaria before the tournament, but it cleared up by the start of tournament. He's 100% now."
Manor Solomon hasn't played since September and Postecoglou confirmed that the winger had another procedure on his knee earlier this week and is still another two or three weeks away from a return.
Another injury concern was Giovani Lo Celso who missed the last three league games for Spurs.
"Lo Celso trained all week but he's missed a fair bit of football so we'll see whether he needs another week or not," the manager said.
"It's probably, for want of a better word, the healthiest squad we've had for quite a while anyway."
Spurs conceded an added-time equaliser at Everton last weekend and lost to a late Nathan Ake goal against Manchester City in the FA Cup, but conceding late is not something that overly concerns their manager.
"It's disappointing to concede goals at any point. People will want to analyse it," Postecoglou said.
"I'm sorry but we're going to be a team that will score or concede goals late. The way we want to close out games is by trying to score goals late on.
"One thing we're not going to do is jump at shadows and try to fix the latest thing being analysed."
