The Soviet Union has in recent months substantially stepped up its efforts to cultivate American sources in Washington and gather information about the Reagan administration, according to informed sources.

The Soviet activity, according to one source, has doubled and perhaps tripled since November, and in response, the Washington FBI office has transferred an additional 15 agents to its 100-member Soviet counterintelligence operation here.

The sources emphasized that the Soviet moves are not necessarily all sinister or geared to recruiting spies in the American government; and the increased activity has little or nothing to do with the Reagan administration's recent hard line toward the Soviets, they said.

But at the same time, the Soviet Union and its allies have been more aggressive and have been making more frequent contacts with people they think may be able to pass them valuable information, ranging from routine diplomatic details to possibly classified data, the sources said.

The cases under investigation range from ambiguous approaches and seemingly routine information-gathering efforts to actual attempts to recruit spies, according to one source.

With every change of administration, foreign intelligence agents accelerate their efforts to identify the key policy makers in the White House and the Pentagon. This time, with the Republican takeover of the Senate as well, the Soviets have more work to do, sources said, and that means more work as well for U.S. counterintelligence officials.

"We are increasing our long-range analytical capability and improving our working relationships with other agencies in the intelligence community," said Theodore Gardner, head of the Washington FBI office. He said the office was also increasing agents' training for counterintelligence.

There are about 250 Soviet block officials in the Washington area who are believed to be connected with intelligence-gathering activities, Gardner said. That number would include hard-core KGB agents as well as persons assigned to routine press-clipping activities or to monitoring congressional committees, Gardner said.

Despite their accelerated efforts, sources said Soviet bloc officials still remain professionally casual in contacts with congressional or White House staff members. "You wouldn't believe now casual," one former FBI agent said. "Usually they meet at some party or perhaps at an office and all that is done in an exchange of cards and perhaps a low-key offer to get together for lunch sometime."

After that, there might be requests for hearing reports and purely public information, the agent said, adding that such benign requests could go on for a long time before any attempt is made to see if classified information can be obtained from the source. "They [the Soviet officials] have got all the time in the world," the agent said.

Intelligence sources said there were a substantial number of what they called active cases involving Soviet intelligence officials and congressional staff aides. Those sources said they could not reveal the names of those staff aides contacted because they would prefer that the Soviets continue the contacts. "There's always the possibility of using our people to provide misinformation to the Soviets," one source pointed out.

Recently, CIA officials were called in to brief Reagan transition team workers about how to deal with any contacts with Soviet block agents. The meeting was called after two workers were taken to lunch by a Soviet Embassy official who, after some pleasantries, reportedly quizzed them about how the National Security Council might operate in the Reagan administration.

The FBI still follows individual Soviet agents at various times, but sources concede it is impossible for the bureau to know about all foreign intelligence efforts, particularly those of the Soviets.

Intelligence sources acknowledge that the FBI often never hears of many of the contacts, in part because many of those contacted either do not realize they are being cultivated or do not know that the FBI hopes to be called when such contacts are made.

Another reason for stepped-up activity is that "the Hill has become so unpredictable that the Soviets have had to pay more attention to it," that source said.

Several sources said there was no indication of any increase in personnel at the embassies of the Soviet Union and its allies. Rather, the embassies are working harder to keep track of the new administration and the new faces in Congress and the bureaucracy.

One source characterized most of the intelligence gathering as benign, adding that he did not see anything wrong with it. "It's when it steps over the line" and becomes blackmail or bribery, "that's when it's important."

In some respects, one observer noted, there is reason to expect Soviet bloc intelligence activities to be less active now than in 1977. "The Russians didn't have the foggiest idea what Carter was all about and what he would do, and they wre understandably concerned," he said. Reagan and Secretary of State Alexander M. Haig, he added, are very much known quantities.