Verniaiev pulled out of last month's European Championships because, according to Ukraine head coach Gennady Sartynsky, he needed to defend his PhD dissertation and recover from minor injuries.
That event in Mersin, Turkey took place from 9-13 December with Verniaiev listed as suspended on 11 December.
Without him, and in the absence of the likes of Russia, Germany and Great Britain on coronavirus grounds, Ukraine won its first men's European title.
FIG has not revealed the reason for the 27-year-old's suspension, saying only that he is "provisionally suspended until the end of the procedure that is currently in progress. The FIG will not comment on an ongoing procedure”.
Head coach Sartynsky told Tribuna.com on Tuesday he had been forbidden from talking about the matter by FIG.
He said, "They said not to say anything yet. When there is a decision, then it will be possible to say something. This is still confidential information."
He added, "What is Oleg doing now? Nothing yet."
He also won gold on the parallel bars, the first Olympic title for Ukraine in gymnastics since Athens 2004.
Just before the European Championships, he spoke to Olympic Channel about his plans for the future and coming back from two surgeries in 2019 as well as having to stop training due to COVID-19 restrictions.