VENICE -- June 2 -- President Reagan has bed, will travel, the White House confirmed today.

He is leaving his horses at home, however, and a spokeswoman for the first lady today denied reports circulating here that Mrs. Reagan did not like the wallpaper in the suite where she and the president will be staying and that because of that it was being repapered in a light blue.

The presidential bed, a king-size made for the Reagans when they visited Portugal in 1985, is being brought out of storage in Lisbon and flown to Venice in time for the arrival of the first couple tonight.

The Reagans will sleep in the bed tonight after they check into Villa Condulmer, six miles outside Venice, where they will stay through Sunday night. On Monday, the Economic Summit begins and Reagan moves to Venice proper to join other summit leaders. Nancy Reagan will fly to Stockholm that day at the invitation of the Swedish government to visit drug and alcohol abuse centers.

The bed flap, however, has been the big news in Venice ever since it was revealed here that the Reagans were bringing their own.

Yesterday, the White House attempted to clarify the situation.

"When {White House advance man} Bill Henkel and others met with the hotel management on a preadvance trip a few weeks ago, they were told that new furniture was being brought in," said Elaine Crispen, Nancy Reagan's press secretary. "But apparently nothing was said about a bed."

The Reagans like to sleep together in a king-size bed, according to Crispen, who said she did not know whether the villa's regular sleeping accommodations are the wrong size or lacking in firmness. Henkel reportedly remembered that Portugal's presidential bed had been made especially for Reagan and was spending sleepless nights there in a warehouse. It was decided to transport it to Venice.

Venetians have also been fascinated by the prospect that Reagan would bring two horses with him for the couple to ride during the four days they will be relaxing in the Italian countryside. The first couple's only scheduled public engagement during the four days is on Saturday, when they will fly to Rome to see Pope John Paul II. The White House last night said categorically that the president is not taking two horses to Venice.

"We never even take Rex {the Reagans' dog} so why would we take horses?" Crispen asked.

Among the other news items titillating Venetians:

The Reagans are bringing their own cook and, as always on international trips, a steward to taste their food.

An unconfirmed story that the first couple will bring along their own electrical generators and an electrician.

A report, also unconfirmed, that the Reagans' hotel has arranged to have two original Canalettos hanging on the presidential walls.

As for the room itself, "If it is repapered, it would be at the recommendation of the hotel manager there," Crispen said. "Mrs. Reagan doesn't like a freshly painted room."

"I just hope at my hotel they have a bed," Crispen added, "because I'm not bringing mine."