The worldwide search for Bradford Bishop, the former diplomat charged with killing all five members of his family in their Bethesda home more than three years ago, is zeroing in on Italy.

For the second time this year, someone who formerly worked with Bishop at the State Department has reported seeing the elusive suspect in the Southern Italian resort town of Sorrento, perhaps as recently as mid-June.

Bishop, who speaks fluent Italian, lived in Italy for six years in the 1960s. He was an Army intelligence officer in Florence, a graduate student in Verona, and an up-and-coming young diplomat in Milan. A former colleague said that while posted at the consulate in Milan during 1963-70, Bishop was temporarily assigned to Naples, which is next to Sorrento.

A policeman in Sorrento said, "We have said that the famous diplomat [Bishop] is not here" now.

In Naples, Romano Argenio, a criminal investigator with the Italian police, confirmed that police received a report "sometime around Easter" that Bishop had again been seen in Sorrento.

Argenio expressed exasperation at trying to catch up with Bishop, however, saying "the press [in Italy] had flee before police could renew a search for him among Sorrento's colorful bars and hotels.

The newspaper Corriere della Sera, the story before the police. The press reports, he said, gave Bishop time to a respected national publication, said in its June 20 Milan edition that Bishop was sighted in Sorrento on March 2 and again in June. It said both sightings had been reported to the FBI.

A spokesman at the FBI field office in Baltimore, which is directing the search for Bishop, said he could not confirm the latest sightings. "But we will be in touch" with Italian police, he said. "We definitely want to follow up on this."

The FBI spokesman said investigators have tracked down countless alleged sightings since the killings on March 1, 1976, but "you have to get excited about those reported by persons who have known Bishop in the past."

The first sighting reported in Sorrento was on Jan. 11, by Roy Harrell, an employee of the Agency for International Development, Harrell worked with Bishop at the U.S. Embassy in Addis Ababa, Ethiopia, in 1966, and at the State Department from 1974 until Bishop vanished.

The FBI and Montgomery County police took seriously Harrell's report, which he filled at the U.S. Embassy in Rome the next day. Harrell said he believes a bedraggled, bearded man he encountered in the public restroom in the Sorrento town square was Bishop.

Harrell, who now is on home leave in Washington from his post in Niamey, Niger, said Tuesday that a friend in Sorrento wrote to him last month that the recent sightings-- they insisted there now were a total of three-- were made by State Department employes who had known Bishop during his tour of duty in Gaberone, Botswana, from 1972 to 1974.

Harrell also recalled Tuesday a conversation with Bishop on the front steps of the State Department on Feb. 26, 1976, during which Bishop told him he was very depressed about failing to win a promotion.

"I told him, there's always next year," Harrell said, "and Brad replied, 'yeah, if there is a next year."

Four days later, according to police, Bishop bludgeoned to death his mother, wife and three sons in their Carderock Springs home, carted their bodies in the back of his station wagon to a swamp in North Carolina, set them on fire, and fled.

Bishop, now 43, vanished without a trace. The station wagon was recovered March 18, 1976, in the Great Smoky Mountain National Park in Tennessee. There were no immediate surviving family members to interview, and police were baffled about a motive for the slayings. Friends and State Department colleagues had described the Bishops as an ideal family.

Harrell said that when he glanced at a man standing at the urinal next to him, in Sorrento last January, he blurted out: "Say, aren't you Brad Bisop?"

The man "began shaking, trembling and backed up from me," Harrell said, "and then, just before he ran, he said, in English, Oh, God, no.'"

When the man ran from the restroom, Harrell said he chased him, but the man quickly disappeared in a heavy rainstorm. Because the rain made it difficult to see, Harrell gave up the chase and set out to catch a bus to Rome. The man he believes was Bishop was wearing greasy clothes, dark pants, probably corduroy, a grubby pullover sweater and had a long, unkempt bear, Harrell said.

Harrell said the sighting occurred about 5:30 p.m., and that when he arrived in Rome about 10 p.m., he immediately telephoned the American embassy to report it. "But the guard didn't consider it important enought to get the duty officer routed up at that time of night, so I went off to bed." "The next morning, Harrell filed a report in person at the embassy. He said he was asked to describe Bishop, and then was shown half a dozen pictures of the fugitive, all of whom he identified as his former colleague.

Arthur Brunetti, security chief at the U.S. Embassy in Rome, confirmed that he and the legal attache [an FBI agent] interviewed Harrell about the Bishop case.

Brunetti said he had read a newspaper account of the later sightings, but had no official involvement. "It's a police matter," Burnetti said.

An added quirk reported by Harrell involved a copy of the Rome Daily American, an English language newspaper, that he said he purchased, but had not looked at, just before entering the men's room in Sorrento last January.

After being unnerved by the brush with a man he is convinced was Bishop, Harrell said he tried to relax on the bus trip to Rome by reading the paper.

"When I came to page 8, there was an AP story, datelined Stockholm, telling of the sighting of Bishop there," Harrell said. The story, under the headline "U.S. Diplomat Hunted Worldwide for Killings," was the first Harrell knew about a reported sighting six months earlier.

"A rather amazing coincidence, to say the least," said Harrell of the events of that day.

Until the Sorrento reports, the Swedish sighting was the closest police came to picking up a trail on Bishop. A woman who said she had known Bishop in Ethiopia told police she twice saw a man she believed was Bishop in a Stockholm park. She recognized him, she told Swedish police, even though he had grown a beard.