Commission Executive Director Patrick McIntyre Jr. wrote a letter saying moving the graves of the 11th U.S. president and his wife, Sarah, will create a false sense of history at the site.
The state Senate has passed a resolution that would move the bodies to the James K. Polk Home and Museum in Columbia, Tennessee.
Polk wanted to be buried at his Nashville mansion, but the residence was demolished after his death.
Polk's father built the home in Columbia where the museum is located.
The bodies can't be moved there without court approval.