Merle Fainsod, director of the Russian Research Center, is presently under consideration for the post of Ambassador to the Soviet Union, the New York Times reported yesterday.

Fainsod is one of many rumored names in the Administration's very extensive search to find a replacement for Llewellyn E. Thompson, Jr., the present Ambassador. Thompson is leaving the post this summer, after spending five years in Russia.

The search has been especially wide in this instance because government officials are not sure of the criteria for choosing a United States Ambassador to Russia. According to the Times article, several different possibilities have been suggested, ranging from a career diplomat to an expert on Russia.

Harriman Mentioned

The Times article said W. Averill Harriman, former Ambassador to Moscow, and Philip E. Mosely of the Council of Foreign Relations, are very high on the list at the moment. Mosely is a soviet specialist, as are Fainsod and Marshal D. Shulman, associate director of the Russian Research Center, who was also mentioned.

Commenting on the question of whether to appoint a career officer, a public figure, or a specialist, Shulman said, "I feel strongly that Fainsod or Mosely would bring a great deal of experience and insight of particular usefulness in this rapidly changing period in Soviet policy."