Kouyate twisted his ankle in the Eagles' 1-1 draw against Southampton but endured to see out the entirety of the encounter.
The 29-year-old has missed just three league matches so far this season, making 17 starts in 21 Premier League appearances.
And Hodgson hopes the midfielder who is one of the regular fixtures in his squad will not be out of action for too long. Also, Wilfried Zaha will serve his one-game after he was sent off at the St Mary's Stadium.
"We've got a couple of players who we need to test tomorrow morning," Hodgson told club website.
"It's not looking that bad but one player who will miss tomorrow is Cheikhou Kouyate because he twisted his ankle during the first half [against Southampton] but carried on for the second half.
"We're hoping it won't be that serious but it will keep him out tomorrow. There is the Zaha suspension but otherwise we've got a full squad."
Crystal Palace are currently placed 15th in the Premier League table with 23 points from 24 matches.