Costinha is expected to start for Albion at home to Leeds as Mats Wieffer faces a lay-off.
The Holland international suffered a knee injury in the 4-3 defeat at Chelsea and will be out until after the next international break.
Former Olympiacos and Rio Ave right-back Costinha has come off the bench in early fixtures and now looks set to get his first chance from kick-off.
Newly-arrived midfielder Chema Andres could be part of the matchday 20 while former Leeds favourite Georginio Rutter and midfielder Yasin Ayari have not been ruled out.
But the game comes too early for recent signing Femi Azeez, who will be assessed again after the weekend.
Jack Hinshelwood, Kaoru Mitoma and Yankuba Minteh remain absent.
Costinha has been bright in his outings off the bench and Hurzeler likes what he has seen so far.
The Seagulls head coach said: “He's a physical player.
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“He is very fit and he's a very clever player, understands the game.
“I'm really pleased with his development so far, I'm really pleased with his attitude. He is an absolute team player.
“He adds great values to this club already in this short period so definitely he can be an option.”
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