"Glenn's fine, he is back training," Hughton told a news conference on Thursday.
"He went for a ball the day before the Nantes game, whacked his back and neck, started the game and probably if he's had another 24 hours he'd have been okay.
"Locadia has been training for a few weeks now and Florin Andone should train tomorrow or Monday."
Romanian striker Andone, who joined from Spanish side Deportivo la Coruna, played 45 minutes for his new club in a friendly against Nice but has since been confined to the sidelines with a groin issue.
The Seagulls will also start the season without winger Jose Izquierdo, who has been given more time to work towards full fitness after his World Cup campaign with Colombia.
Hughton was pleased with the club's close-season transfer business, having recruited talented youngsters like Yves Bissouma, Bernardo and Alireza Jahanbakhsh for a club record fee.
"We've brought in some young players for the Under-23s and seven first team players - but we've lost faces too," the manager said. "But at the moment and I'm happy with our work.
"I think we have a stronger squad than this time last year - we've brought down the overall average age too. That's with no disrespect to previous squads, though."
Brighton, who finished 15th last season, visit Watford on Saturday.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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