Many of the clubs face considerable infrastructure difficulties and are struggling to meet administrative, legal and financial conditions laid out by European football's governing body UEFA.
"There are seven teams who are on the brink and could disappear," Dragomir told local media without naming any clubs.
"Their debts are so big that even the TV money could not save them."
Eighteen-times Romanian champions Dinamo Bucharest and city rivals Rapid are two of nine European clubs facing punishment from UEFA over arrears to other teams, their staff or tax authorities.
"Hopefully someone will let us know what's happening and what will happen with the club and with us," said Rapid captain Daniel Pancu as local media reported The Railwaymen's players had not been paid for several months.