Onorato, with 40% of Italian ferry group Moby, has been keen to bring the two companies together.
But shareholders want any tie-up to benefit both sides.
They also fear a merger would lead to cutbacks of ships, routes, crew and shore staff.
Both companies have had to sell off 10% of capacity on routes to Sardinia because of antitrust rulings.
The Clessidra fund owns 35% of CIN and 32% of Moby.
CIN
