The Italy international was an early withdrawal in his side's 2-0 beating of Fulham two Mondays ago and subsequently sat out the Lilywhites' victory over Crystal Palace last Friday.
Udogie — who is understood to be nursing a muscular issue — had started each of Spurs' first nine Premier League fixtures under Postecoglou and has made an immediate impression, setting up two goals in the top flight so far.
Without the former Udinese man in the fold, Tottenham fielded Ben Davies on the left-hand side at Selhurst Park, but the Wales international was then withdrawn for Emerson Royal at the break.
Tottenham struggled to get going for long periods of their meeting with Palace, but a Joel Ward own goal and Son Heung-min strike in the second half proved decisive before Jordan Ayew's consolation.
Offering an injury update to Tottenham's media channels ahead of the visit of Chelsea on Monday, Postecoglou confirmed that Udogie was «progressing» but could not guarantee he would be available to face the Blues.
«We'll see how he's progressing, there's still a few days before the Monday game, he's progressing through it and we'll assess him closer to it. Everyone else is OK,» Postecoglou said.
Davies was the natural pick to deputise for Udogie at Selhurst Park, but the 30-year-old then sustained a fresh ankle knock in the first half, forcing Postecoglou to field Emerson on the left flank for the second period.
The Spurs boss conceded that Davies would likely not be available to tackle Chelsea in the London derby, having not welcomed him back for team
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