William Bradford Bishop Jr., the missing State Department official who is charged with killing five members of his family in their Bethesda home in 1976, reportedly was seen in Italy five months ago.

FBI officials in Baltimore said yesterday that agents had interviewed a State Department employe who reported seeing Bishop on Jan. 11 in the southern Italian resort town of Sorrento.

At that time, American and European newspapers were carrying reports that Bishop - who vanished after his mother, wife and three children were beaten to death - had been seen twice in Stockholm, Sweden in July 1978.

A spokesman for the FBI field office in Baltimore said the agency is working with Italian authorities to determine the validity of the latest sighting.

In the three years and three months since Bishop disappeared, police have checked out hundreds of reports that Bishop had been seen. The reports came from areas around this country and in Europe and Africa, where he had been stationed as a foreign service officer in the 1960s.

The tips from Sweden and Italy, however, were the first to come from people who knew Bishop personally. A family friend reported seeing him in a Stockholm park last July.

Bishop, 43, speaks both Italian and Serbo-Croatian fluently. He lived in northern Italy on three occasions - in Verona from 1961 to 1963 as an officer with Army intelligence; in Florence as a graduate student in 1963 and 1964, and as a diplomatic envoy in Milan in 1968 and 1969.

Details of the latest report about Bishop were made public yesterday by Gary Reals, a reporter for WMAL radio. Reals said the man who allegedly spotted Bishop had been a coworker with him at State both in Washington and abroad, and had seen Bishop here in February, 1976, two weeks before the slayings.

The witness, who is assigned to a diplomatic post in Africa, was vacationing in Sorrento. According to Reals, the witness was in a public rest room at a large square in Sorrento when a bearded, bedraggled man walked in. The witness immediately recognized the man as Bishop.

The witness called out "Bradford Bishop" or "You're Bradford Bishop," Reals said. The bearded man then fled outside, where he disappeared in a blinding rainstorm.

The appearance of the bearded man spotted in Sorrento was in marked contrast to that of a man, also bearded, who was seen in a park in the Swedish capital city six months earlier. The woman who identified this man as Bishop described him as neat and well dressed.

The man in the public rest room in Sorrento however, had an unkempt beard, was wearing disheveled clothing and looked like a hobo, Reals reported.

An FBI spokesman said last night that agents have known about the Sorrento sighting for several months, but that no new information has been developed.

Bishop's trail went cold almost immediately after the murders of his family. On March 2, 1978, the bodies of his wife, Annette, 37, his mother, Lobelia, 68, and his three sons, Bradford III, 14, Brent, 10, and Geoff, 5, were found in a remote section of eastern North Carolina.

It took North Carolina and Montgomery County officials a week to identify the bodies. Montgomery County police later determined that the family members had been bludgeoned to death at their home in the Carderock Springs subdivision of Bethesda.

Police theorized that the bodies had been loaded into the family station wagon and driven to North Carolina, then taken to a remote swamp, dumped in a makeshift grave and set afire.

The last confirmed sighting of Bishop was on March 2, 1976, the day after the killings. That day, police said, Bishop used his Texaco credit card to buy $15 worth of supplies in a sporting goods store in Jacksonville, N.C.

Bishop's station wagon was recovered on March 18, 1976, in a remote campground in the sprawling Great Smoky Mountain National Park, several hundred miles inland, on the North Carolina-Tennessee border. CAPTION: Picture, WILLIAM BRADFORD BISHOP . . . sought in five slayings; Map, no caption.