The Lilywhites return from the international break aiming to right the wrongs of their shocking 3-2 loss to Brighton & Hove Albion two weekends ago, where they let a 2-0 lead slip in the second half.
Spurs were without their skipper Son for that defeat on the South Coast, as the South Korea international was recovering from the thigh injury he picked up against Qarabag in the Europa League in September.
Meanwhile, the luckless Richarlison has not played since August 24 due to a calf problem, and Postecoglou told the media last month to refrain from asking about the Brazilian until he delivered an update himself.
Spurs were also dealt a concern over the young Bergvall during the international break, as the 18-year-old picked up a calf injury in Sweden training and was sent home before their 3-0 win over Estonia on Monday.
Son expected to make Tottenham return against West Ham
However, speaking to Spurs' media channels on Thursday, Postecoglou played down the seriousness of Bergvall's concern and also revealed that Son and Richarlison were on track to be available for the lunchtime derby.
"The main ones, Sonny and Richy have done some good work and trained with the group, which is a real positive for us," Postecoglou said.
"Sonny was always hopefully going to get through this international break and be ready, and Richy's done some good work, so hopefully both available for the weekend.
"International guys, I think just about all of them got through OK, we're still waiting on a couple to come back into the building. Lucas was the only one that had a slight niggle but we're hoping he'll be OK."
With all of Son, Richarlison and Bergvall on course to feature this weekend, Tottenham's only injury absentee should be Wilson Odobert, who is recovering from the thigh problem he sustained against Coventry City in the EFL Cup last month.
Postecoglou provides update on Wilson Odobert fitness
The summer signing from Burnley was initially thought to have been in with a slight chance of coming back this weekend, but Postecoglou has now confirmed that will not be the case.
However, Odobert could be available again next week, when Tottenham take on AZ Alkmaar in the Europa League on Thursday night before travelling to Crystal Palace for another Premier League London derby on Sunday.
"Really it's only Wilson, who also has done some good work over the last couple of weeks and hopefully joins the main group at some point next week," Postecoglou concluded.
Son's return to fitness could see Postecoglou make one change to his starting lineup for the visit of West Ham, as the South Korean should replace Timo Werner on the left-hand side of the attack.
Spurs sit ninth in the Premier League standings ahead of Saturday's lunchtime kickoff, but they could be overtaken by their 12th-placed opponents, who are just two points worse off after seven gameweeks and won 2-1 at the Tottenham Hotspur Stadium last December.