The former Manchester United forward has hit the ground running since returning to England from Germany's Bayer Leverkusen and will look to add to his three league goals for the club.
"It's not a big thing," Bilic told a news conference on Thursday. "He trained a couple of days ago... felt a little bit of a tight hamstring, we scanned it, which is very important and scan was completely clear.
"He only missed yesterday's training, which was a light session and he will train today and we are expecting him, based on the scan and his feeling, he will be ok."
West Ham will be without defender James Collins, who has an ankle injury and forward Diafra Sakho who is suffering from back pain after the club's 1-1 draw with Burnley last time out.
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The London side are 15th in the table with eight points from eight games while Brighton are a spot above them with a similar record but a better goal difference.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond)
