The Lilywhites boarded the flight to Hungary seeking to make it two for two in this year's revamped competition, having overcome Radu Dragusin's early red card to defeat Qarabag 3-1 on matchday one.
The triumph over the Azerbaijani giants preceded an emphatic 3-0 Premier League victory over Manchester United, who were torn to shreds by Postecoglou's side even without the services of captain Son.
The South Korean attacker had picked up a knock in the Qarabag success and was not deemed fit enough to turn out at Old Trafford, where left-back Udogie was taken off at half time due to a quadriceps problem.
Postecoglou insisted that the defender's problem was not severe, although having had surgery on his quad towards the end of last season, the Tottenham boss has unsurprisingly erred on the side of caution this time around.
Son, Udogie ruled out of Tottenham's clash with Qarabag
Speaking to SPURSplay before his pre-game press conference, Postecoglou announced that Son and Udogie had both been left at home to continue their rehabilitation, but there are no fresh concerns from the win over Man United.
"Sonny and Destiny are back in London. They're working away, but they're not available for this one. Everyone else from the weekend got through the game and is good to go," Postecoglou said.
Son and Udogie are two of five Tottenham absentees for the showdown with Ferencvaros, as Wilson Odobert (thigh) and Richarlison (calf) are also missing, while Dragusin serves his one-game suspension following his early dismissal on matchday one.
The clash with the Hungarian giants is a prime opportunity for Postecoglou to hand minutes to fringe players and academy prospects, and one player who falls into the former category is exiled left-back Sergio Reguilon, but he will not be involved in Budapest despite travelling with the team.
The former Sevilla man has not played a single minute for Tottenham this season and has only made one matchday squad, being an unused substitute in the EFL Cup third-round win over Coventry City.
Postecoglou reveals reason for Reguilon inclusion
Reguilon was not included in Spurs' Europa League squad and is therefore not eligible to play on Thursday evening, so his selection naturally raised a few eyebrows.
However, Postecoglou said that the Spaniard's call-up was merely for practice purposes, saying: "We've got training sessions (here), so we've brought young players and Reggy, just to make sure the quality of our training is what it needs to be today."
With Udogie absent and Reguilon ineligible, Ben Davies is likely to get the nod on the left-hand side of the backline, having played the full 90 minutes in the triumph over Qarabag.
Fraser Forster, Archie Gray and Lucas Bergvall - who was taken off after just 12 minutes against Qarabag due to Dragusin's red card - are also likely to be promoted to the starting lineup, while young stars Mikey Moore and Will Lankshear will be in contention for minutes too.
While Tottenham have never faced Ferencvaros before, Postecoglou met the Hungarian champions in the 2021-22 Europa League while in charge of Celtic, masterminding a 3-2 away win and 2-0 home victory.