The Soviet Union recently suggested a secret channel of communications to the Reagan White House in an effort to reopen substantive contacts but the offer was promptly rejected by Washington, according to well-informed sources.

In a gambit that recalls the secret dialogue during the first years of the Nixon administration, the Soviets reportedly made the overture in the apparent hope that a secret back channel would draw the new administration into communications on East-West relations and arms control issues despite President Reagan's anti-Soviet rhetoric.

The U.S. rebuff reportedly has led Soviet officials to take on face value Reagan's public pronouncements and has strengthened the impression here that the United States has lost interest in peaceful working relations with the Soviet Union.

The suggestion of a secret back channel -- an informal method of communications that bypasses formal channels -- reportedly was advanced by Georgy Arbatov, the Kremlin's top specialist on U.S. affairs, in talks with several U.S. business executives visiting here recently. It came after the Reagan administration had spurned several public offers including those made by President Leonid Brezhnev.

When it was relayed to Washington, Arbatov's reported overture is said to have annoyed senior U.S. officials.

The American charge d'affaires here, Jack Matlock, was told to see Arbatov, who heads, the Institute of United States and Canadian Studies and is a member of the Communist Party's policy-making Central Committee, and formally decline the offer. The United States would continue to rely on official channels, which are adequate, Matlock told Arbatov, according to the sources.

Both Arbatov and Matlock have refused to discuss the matter but Soviet and U.S. sources privately substantiated the account.

Henry Kissinger, while serving as presdient Nixon's national security adviser, established a back channel of communications through Soviet Ambassador Anatoliy Dobrynin. In his memoirs, Kissinger said that the channel was designed to skirt bureaucratic indiscipline, news media and congressional pressures and give him direct access to Brezhnev.

It was used to "privately clarify the purposes" of the two governments before major issues were moved to the conventional channels. It bypassed the secretary of state and other senior officials. When formal talks reached deadlock, the channel would be opened up again. Once it included a clandestine visit to Moscow by Kissinger to prepare the 1972 summit.

Arbatov's reported overture may have been designed to reactivate this channel with himself as the conduit and give Reagan an opportunity to privately define his purpose on Soviet-U.S. issues and especially arms control without endangering his anti-Soviet reputation.

Both sides now appear eager to put the best face on the incident. Diplomatic sources here quoted Arbatov as saying that he had never made the overture and U.S. diplomatic sources suggested that the originial messages may have been garbled.

According to an American executive's account of his conversation with Arbatov some weeks ago, the Soviet official made the suggestion when he said that in these difficult times the Americans may want to have private access to the top men in the Kremlin.

The executive quoted Arbatov as saying that if the Americans wanted such access, Arbatov was prepared to serve as a confidential back channel.

Other U.S. visitors have reported similar suggestions by Arbatov.

Another U.S. executive, who visited here after the offer had been rejected, quoted Arbatov as saying that Matlock not only relayed the insistence on the use of official channels but also told Arbatov that "it was not necessary for him to carry on discussions with Americans independently."

There was speculation among Western diplomats that Arbatov's reported overture might reflect rivalry that is said to exist between him and Dobrynin.

But knowledgeable Soviet sources dismissed such speculation.