There may be probate records for his father's estate where he is named; it is exceptionally unlikely that he was born in Monroe County as it did not exist until 1819, being formed from lands ceded by the Cherokee under the Calhoun Treaty. So you'd have to find out where the probate records would be (since they're held by the county courthouse); 1786/87 is exceptionally early for Tennesee; as Samuel Henderson gives his birthplace consistently as Tennessee in the 1850 and 1860 censuses it's likely he was born in Knox County/Knoxville (which was the major settlement in what would become the state of Tennessee at the time he was born).
There appears to be a published genealogy of Samuel Henderson's descendants; it does not, however, name his parents.
