The Nobel Peace laureate and the beatified nun headed Calcutta's Missionaries of Charity for the sick and the abandoned until her death on September 5, 1997.
Albanian Prime Minister Sali Berisha has said the remains should be repatriated before the 100th anniversary of Mother Teresa's birth next August, The Times of London reported.
However, Indian church and state officials in Calcutta are irate over calls to exhume her body, the report said.
An Indian Foreign Ministry spokesman told The Times: "Mother Teresa is an Indian citizen and is resting in her own country."
There is also concern that Macedonia could become another claimant to the remains, the report said.
Mother Teresa' parents were ethnic Albanians but she was born in 1910 in Skopje, which was then part of the Ottoman Empire but is now the capital of Macedonia.
Mother Teresa once said: "By blood, I am Albanian. By citizenship, an Indian. By faith, I am a Catholic nun. As to my calling, I belong to the world."