REYKJAVIK, Iceland (AP) _ U.S. and Soviet officials began touring Reykjavik today in search of a ''cozy little place'' for the superpower summit.

The Iceland government favors the Saga Hotel, the capital's most luxurious, as the site for the Oct. 11-12 meeting between President Reagan and Soviet leader Mikhail S. Gorbachev.

But also under consideration are a sports hall, an art gallery and a museum of reconstructed old Icelandic houses, Hugh Ivory, head of the U.S. Cultural Center in Reykjavik, was quoted as saying.

The daily Morgunbladid newspaper quoted Ivory as saying both sides were looking for ''a cozy little place where the leaders can talk in peace. They don't want to sit alone in some huge hotel.''

Ivory declined to comment on possible locations when contacted later, saying various possibilities were under consideration.

Only a few officials from the Soviet Union and United States have arrived so far. The main advance parties are expected to arrive late today.

The island of 240,000 inhabitants faces what Morgunbladid called ''a gigantic task'' - arranging in 11 days a superpower summit that will be the focus of world attention.

The newspaper ran a cartoon showing Prime Minister Steingrumur Hermannsson welcoming the superpower leaders into a dingy looking living room and saying, ''You are most welcome to stay, gentlemen, but I hope you like my cooking.''

It showed a pot with a whale's tail boiling on a stove.

After initial bewilderment at their country being chosen for the summit, Icelanders began to pick up the spirit of the occasion. Henson Co., a clothes manufacturer, began marketing T-shirts with pictures of the two superpower leaders at 685 krona ($17) each.

With hotel rooms at a premium, Icelanders were urged to offer private rooms for rent, and U.S. television networks reported some offers of houses at $3,000 a night.

The networks and the Soviet government were chartering ocean liners to berth in Reykjavik harbor in an effort to accommodate journalists.

Reykjavik has 1,500 hotel beds, and the government has sequestered the four best hotels under special powers provided by the constitution.

Judging by past summits, the island can expect several hundred officials and as many as 3,000 journalists to flood Reykjavik in the coming days.

Icelandair, the privately owned national airline of four DC8s and two Boeing 727s, said it was adding extra flights from London; Copenhagen, Denmark; Luxembourg and New York.

Public relations manager Margret Hauksdottir said the number of extra flights would depend on demand. ''It's quite a lot busier than usual. ... We're quite out of the way but I wouldn't say it's difficult to get to Iceland.''

Icelandair is the only scheduled airliner serving Iceland.