The Seagulls were without eight players due to either injury or illness for the 4-2 defeat away against Chelsea last weekend - Hurzeler's first defeat since taking the reins in the summer.
Star striker Joao Pedro has been dealing with a couple of injury issues at the start of this season; he suffered a knock on international duty with Brazil last month and was absent for two Brighton games before returning for the 2-2 draw with Nottingham Forest a fortnight ago.
However, the 23-year-old picked up an ankle injury towards the end of that match following a strong challenge from Morgan Gibbs-White and he was seen using crutches after watching the defeat to Chelsea.
Hurzeler has since revealed that Pedro is one of three "long-term" injury absentees along with midfielder Matt O'Riley and defender Jan Paul van Hecke, who are sidelined with respective ankle and groin problems.
Hurzeler delivers Brighton injury update
However, the Brighton boss has provided a positive update on Brajan Gruda (unspecified), Solly March (knee) and James Milner (hamstring), who could all be fit to return this weekend after taking part in training.
Gruda is yet to make his debut for Brighton since completing his £25m summer transfer from Mainz 05, while March is on the verge of making his first appearance for the Seagulls after almost 12 months on the sidelines.
Speaking at a press conference on Friday, Hurzeler said: "Let's start with the positive things, Brajan Gruda and Solly March - they trained, they trained really good this week, they might be an option for the weekend.
"The long-term injuries are Matt O'Riley, Joao Pedro, JP (Van Hecke), they are still missing... I'm forgetting someone... James Milner, he might be an option for this weekend.
"In terms of Van Hecke I don't think his injury is that bad but you go from week to week. Matt O'Riley is very positive and he's making small steps forward and I think that's very important when you have a bad injury.
"He's sticking to the plan after his surgery. He's doing his rehab and we're looking forward to seeing him back on the pitch.
"So overall, I think positive and negative news but in general more positive with the players coming back."
Veltman fit, but Adingra remains a doubt
Meanwhile, Hurzeler has confirmed that defender Joel Veltman will return to the matchday squad after missing the defeat to Chelsea through illness.
Simon Adingra, however, remains a doubt and will be assessed ahead of kickoff after the winger was left out of last weekend's game as a "precaution".
"Joel will be back," said Hurzeler. "Simon, we have to be careful. We have to look how it's going and then we have to make a decision."
Brighton currently sit ninth in the Premier League table, one point and one place behind Sunday's opponents Spurs, who beat Manchester United 3-0 last weekend but lost 4-2 at the Amex Stadium last season.