The courtships come in response to New York's new, tougher gun control laws.
Lawmakers from Michigan, South Carolina, Arizona, and Oklahoma have all sent letters to Remington's owner, Freedom Group, since New York passed tougher gun control legislation a few weeks ago. Texas first contacted the company back in November.
In a letter, South Carolina Representative Jeff Duncan says his state believes in the right to keep and bear arms.
Remington employs about 1,200 people in the Mohawk Valley town of Ilion making rifles, including the Bushmaster semi-automatic, now prohibited in New York.
Local union representative Frank "Rusty" Brown says it's a "horrific" situation. "This is actually the worst situation we've been in as far as, you know, other states wanting to lure us away."
Brown says his union signed a new five-year contract with the company in December.
New York State has given Remington close to $6 million in incentives since 2009.
Remington has not responded to requests for comment.
Reporting by the Innovation Trail is supported by the Corporation for Public Broadcasting. Visit innovationtrail.org.