Earlier reports indicated both would miss the remainder of the campaign in a blow for the Gunners in the Premier League title battle with leaders and favourites Manchester City.
"With William, that’s for sure that he’s not going to be fit for this game and we are doubting whether he will be for the next game (at Nottingham Forest) as well," Arteta told reporters on Friday when asked about their injury status.
"But we want to keep the hope going and make sure that we give ourselves the best chance to bring them back."
Saliba has been out since March with a back injury while Zinchenko came off with a suspected calf issue during the second half of Arsenal's 2-0 win at third-placed Newcastle United last weekend.
Arsenal have three matches remaining and are one point behind City, who have a game in hand and have been in the driving seat since beating the North Londoners 4-1 at the Etihad on April 26th.
Since then Arsenal have beaten Chelsea and Newcastle.
"Every time you win, every time you play well, every time you feel like you’re competing at a level that is required to win this league, it gives you hope," said Arteta.
"It’s not in our hands and on Sunday we’re certainly going to need to be at our best again and try to win the game. If we win the game, we will be a little bit closer.
"There’s three games to go, this is the crucial one and right now we want to beat them and elevate our hopes and enthusiasm to keep going because everything is still to play for," added the Spaniard.
Arteta said Brighton manager Roberto De Zerbi and his staff were doing a remarkable job and expected Brighton to be very tough opponents.
Arsenal beat Brighton 4-2 when they met on the South Coast at the end of December after losing 3-1 in the third round of the League Cup at the Emirates last November.
