The vacancy was created after S K Roy resigned in June, nearly two years ahead of his retirement as chairman of the insurance firm.
Sharma has been shortlisted for the post of chairman and the Appointments Committee of the Cabinet headed by Prime Minister Narendra Modi will take a final call, sources said.
If ACC approves Sharma's appointment, he would get three years term, sources added.
Sharma, at present a managing director with the insurer, was given the additional charge as chairman after former chairman S K Roy was relieved of his duties last month.
More From This Section
He also served as the chief executive of its mortgage subsidiary LIC Housing Finance and zonal manager in charge of the south zone.
Roy, appointed by previous UPA government, had resigned nearly two years ahead of completion of his five-year term. He was serving as the chairman since June 2013.
Roy joined Life Insurance Corporation of India in 1981. On May 31, 2013, he assumed charge as Managing Director of LIC. Prior to his elevation, he was head of the International Operations division.