A reduced capacity of 14,000 may be in effect for England's one-day international against Australia at Headingley later this year.
The ground's rugby stand could be forced to close for safety reasons.
Ticket sales for seats in the stand have already been suspended, according to a local media reports.
Mark Arthur, the boss of Yorkshire, who plays at the ground, has explained the area may not be used again over the next two years.
"The upper-floor balustrade at the front of the balcony has been condemned, awaiting a further structural engineer's report," he said.
"It's basically corroded at the front of the stand - some of the plaster has come off the front of the balustrade, and it's just not safe.
"If somebody leaned against the front of the balustrade, they could fall straight over and straight down."
Headingley is scheduled to host England's match against Australia on September 11.
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