In a mixed update on the fitness of his squad, Postecoglou confirmed midfielder Bissouma had suffered a groin tweak while on international duty with Mali.
But centre back Micky van de Ven and striker Dominic Solanke, the Premier League's most expensive signing of the summer at £65million, are in line to return.
Van de Ven featured against both Leicester and Everton but after sustaining a knee problem in the latter match, he was forced to sit out against Newcastle.
Solanke, meanwhile, damaged his ankle on his debut but has since trained.
Tottenham boss Ange Postecoglou has delivered an injury update for the north London derby
On Bissouma, Postecoglou said: 'It's hard to say at the moment, it's a tweak in his groin. The initial reports are it's not serious which means there is a chance for Sunday, which tells me it's nothing significant.
'If he doesn't make Sunday, then I'll assume he'll be right for after that. At the same time, he's just come off a long flight, you never feel great anyway, we'll see how he trains tomorrow and that will give the best indication.'
Van de Ven is 'feeling good', Postecoglou has confirmed, and the defender is expected to start at the Tottenham Hotspur Stadium on Sunday.
'He's trained all the way through the international break, and it was good for him to stay with us to build him back up so he's ready to go,' Postecoglou added.
Ace Solanke is a step closer to making his belated second appearance for the club, which could even come against Arsenal with a late call to be made.
Postecoglou said: '[He's] improved as well and trained the back half of this week. We still have two days to go with those guys, so hopefully, they get through training OK.'
Arsenal have also suffered in the injury department with captain and talisman Martin Odegaard likely to miss several weeks after injuring his ankle while with Norway.
Mail Sport reported Odegaard would undergo further tests to determine the extent of the issue - but he has not yet been officially ruled out of action this weekend.
Declan Rice will also be absent against Spurs, having been shown a red card for his bizarre involvement in a spat with Brighton defender Joel Veltman a fortnight ago.