President Reagan is considering asking Sen. Charles H. Percy (R-Ill.), outgoing chairman of the Foreign Relations Committee, to undertake a special mission to India, and some administration officials said yesterday there are rumors that Percy, who was defeated for reelection Nov. 6, might be offered the post of U.S. ambassador to that strife-torn country.

Percy could not be reached for comment. An aide who asked not to be identified said the senator had discussed with the White House "various possible posts of a foreign-policy nature," but the aide refused to identify them and said Percy has not decided whether to stay in government.

White House and State Department sources said the administration has been weighing the desirability of sending a special high-level mission to India, where religious strife between Hindus and Sikhs reached crisis levels after the Oct. 31 assassination of Prime Minister Indira Gandhi. The sources added that Percy, who has a long-time interest in India, had expressed interest in undertaking such a mission.

However, the sources said, there has been no decision about whether a special mission should be sent.

They also said it was not clear whether the rumors about Percy becoming ambassador resulted from confusion about his possible involvement in a special mission or whether the administration is actively considering him as a replacement for Ambassador Harry G. Barnes Jr., a career Foreign Service officer.