The contacts were made following information received by the Independent that the five-man Board of Pardons and Paroles would have granted clemency if the Prime Minister had intervened.
Two diplomatic lines of communication were set up by the board, which assumed that the British Government would intervene, but one official involved in the decision-making process said last night: "We waited and waited but the call never came."
J. Wayne Garner, the chairman of the board, emphatically denied last night that Mr Major's intervention would have saved Ingram, but the source said it had been decided to say publicly the Prime Minister could have made no difference.
Mr Major had refused to intervene, arguing that he had no "proper grounds" to make a plea for clemency, but last night Geoffrey Robertson QC, a top human rights lawyers, called for an inquiry into the legal advice on which the Prime Minister made his decision.
The Independent's source in Georgia said: "If John Major had written in his capacity of Prime Minister of your government, that would have been viewed as an unprecedented and momentous intervention.
"The members of the board take an oath to do their best to consider the welfare of the citizens of Georgia but that must sometimes be viewed on a higher plane than the issues of fact in one criminal prosecution.
"Sometimes we must consider Georgia's place in the family of nations." This was a reference to Atlanta's role in hosting the Olympics next year.
The board's director of legal services, Christopher Hamilton, refused to confirm or deny that Mr Major's intervention would have changed its mind.
However, he did say: "We had established channels of communication with the Department of State and the international division of the Department of Justice . . . We waited and watched in readiness for a message [from Mr Major] but that never came."
Two calls were made to the board last night, one from a British consulate official and the other from a senior Washington embassy official. It is understood they were trying to establish what influence could still be wielded by Mr Major. Downing Street last night repeated its line that Mr Major had believed there were "no proper grounds" for intervention. Sources said there had been no indication that an intervention would save Ingram.