A number of informed Western sources here have reached the cautiously optimistic opinion that the criminal trial of American businessman Francis J. Crawford, due to begin in Moscow City Court today, could possibly end with a quick conviction and expulsion designed to minimize the case's adverse impact on Soviet-American relations.

These persons lack direct knowledge of Soviet intentions in the 11-week-old case, which is widely viewed among foreigners here as a retaliation for the jailing of two Soviets in New York on espionage charges.

Crawford and three Soviets are accused of illegal currency dealings. If convicted on a charge of selling $8,500 illegally, the 37-year-old Alabaman could face up to eight years in a labor camp.

The sources base their hopes for the fate of the International Harvester representative on at least three publicly known factors: Recent comments by American oilman Armand Hammer predicting such an outcome after Hammer spoke personally with Soviet leader Leonid Brezhnev; the visit of Sen. Edward M. Kennedy (D-Mass.), to the Soviet Union which began yesterday; and the reported pretrial concerns of Crawford's Soviet-appointed lawyer.

Two weeks ago, Hammer said he believed that Crawford would be convicted but quickly expelled from the Soviet Union. Yesterday, it was being said by knowledgeable sources that Kennedy, seen by the Soviets as an especially powerful and influential figure in America and a man with his own special relationship wit Brezhnev, could have come here now only after receiving ironclad assurances from high-ranking Soviets that the senator would not be embarrassed politically by the outcome of the Crawford trial.

Kennedy is visiting as senior adviser to the American delegation to a World Health Organization conference in Alma Ata in Soviet Central Asia. He flew from Moscow to Tashkent last night and today will go to Alma Ata. He is to return to Moscow at the end of the week.

The Kennedy visit comes at a time when the Carter administration has stopped all high-level visits by administration officials in retaliation for the Soviet trials in which dissidents Yuri Orlov, Alexander Ginzburg and Anatoly Scharansky were given stiff sentences.

Crawford's Soviet lawyer, Leonid Popov, has reportedly been urging his American client not to introduce new material into the trial or impeded the pace of the trial in any way. Some here have interpreted this to mean the Soviets are anxious to go through the motions and expel Crawford, perhaps this week.

Those expressing such optimistic views readily concede that their perspectives may be affected as much by groundless hope as by any hard-edged portents offered by the inscrutable Soviets. The arrest June 12 of the Harvester products manager created more tension and apprehension within the small resident American community than any other single event of the summer.

The trial of the two accused Soviets is scheduled to begin Sept. 12 in New Jersey.