World City Corporation has signed an agreement of intent with four German shipyards to build the giant Phoenix vessel, tentatively scheduled for delivery in 1992.

It is estimated that the cost to build the 5,600- pax, 260,000-ton cruise ship will be about $1 billion at today's exchange rates.

According to Knot Utstein Kloster, President of World City Corporation, the four yards are Howaldtswerke Deutsche Werft, Bremer Vulkan, Blohm + Voss and Thyssen Nordseewerke.

World City Corporation has raised $200 million in equity financing in the United States and is now working with the yards to complete the financing so that a building contract can be signed before the end of the year.

Conflicting reports say that the order is not dependent on subsidies from the German government.

The construction is estimated to take four years. A broad range of European suppliers have already been consulted and have submitted bids.

When the Phoenix concept was created about five years ago, Kloster was also negotiating with German yards, but has more recently been dealing with the Japanese yards of Ihi, Mitsubishi and Nippon Kokan, which now seem to be out of the picture.

But there is considerable skepticism among cruise line executives and shipping press whether the Phoenix will ever rise.

Kloster, however, has separated himself from the rest of the Kloster cruise business, and is devoting himself fully to the Phoenix. He expects the overall financing to be generated by multinational companies taking $1 million units in the project in return for certain rights of usage of the ship.

The naval architect is Tage Wandborg of the Danish firm, Knud E. Hansen.

The company board also includes attorney Ole Lund of Oslo, Norway; Peter V. Ueberroth; and attorney John S. Rogers, senior partner in Burlingham, Underwood & Lord of New York. Rogers coordinates the day to day operations of the company. World City has offices in Oslo and New York.

The Phoenix will sail Caribbean cruises from a South Florida port and will fly the Norwegian flag.