The proposal could appear on the parliament's agenda, and following a vote by the MPs the case could forward the proposal to the Citizenship, Migration and Society Consolidation Committee. Following a decision by the committee, the Saeima would have the final say on the matter.
Baryshnikov, a US citizen, was born in Riga in 1948 and started attending ballet classes at the age of nine. He further pursued his career in Russia but emigrated from the country in 1974.
Should he be granted and willing to accept the citizenship, both US' and Latvian legislature permits people to hold a double citizenship.
Similar rumours circulated some years ago with regard to granting citizenship to Garry Kasparov, though no citizenship was granted despite a campaign by his supporters. However in Baryshnikov's case he has the added advantage of having been born in Riga.
The rumors appeared to be borne out Thursday with a proposal registered on the Saeima's website to grant Baryshnikov citizenship.
The application, registered late on December 21 was signed by 12 members of parliament from all parties including parliamentary speaker Inara Murniece.
The application comes complete with a letter from Baryshnikov himself in Latvian in which he says "Thank you for the invitation from the Republic of Latvia to consider taking Latvian citizenship" and says he has considered the mattered "with the greatest humility" and that his first 16 years living in Latvia provided the basis for the rest of his life.
"It was there that my exposure to the arts led me to discover my future destiny as a performer," he says.
"Riga still serves as a place where I find artistic inspiration" he says, before expressing his willingness to accept citizenship is offered, saying: "I am truly humbled to receive such a high honor from the Republic of Latvia, and if accepted as a citizen I will uphold hat honor with conscientiousness and pride."
Attached to the document is also a declaration signed by Baryshnikov saying there is no impediment to him receiving Latvian citizenship.