In a statement put out Friday, Cooper said he wants to stay in office in Raleigh rather than contest the Senate post.
"While I am honored by the encouragement I've received, I don't want to go to Washington and serve as a U.S. Senator at this time. I am committed to public service and I want to serve here in North Carolina rather than in Washington," said Cooper, who was re-elected to a third four-year term in November.
Cooper was re-elected to a third four-year term in November, and after three successful statewide campaigns, Cooper was considered to have a strong chance to unseat Burr - a single-term incumbent - next year.
Burr was previously a congressman from the Winston-Salem area.