The centre-back, who signed from Rennes in a £28million deal earlier this summer, was forced off after just 23 minutes at Ibrox because of an ankle problem.
An X-ray confirmed the Moroccan international has not suffered a break but speaking after the 3-1 loss, manager David Moyes said he feared the 26-year-old could have ligament damage.
“We’ve already had Nayef X-rayed and there’s no break in his ankle, which is good news,” Moyes said. “It might be some ligaments, or he’s twisted his ankle – it blew up immediately so we have to hope it’s not a problem.”
The Hammers will wait for Aguerd’s swelling to go down before carrying out further examinations, with their Premier League opener against champions Manchester City only two-and-a-half weeks away.
Moyes currently has five senior centre-halves in his squad, but Craig Dawson has been struggling with injury during preseason, while Angelo Ogbonna is only just back having been out with an ACL problem since last November.
The Hammers were ready to let Issa Diop leave the club this summer should their asking price of close to £20m be met, with Fulham interested in the French centre-back.
However, should Aguerd’s injury prove serious, Moyes may be forced into a rethink and the Scot will be wary of a repeat of the defensive injury crisis that threatened to derail West Ham’s campaign last term.