Article 1, Section 8,
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings;—And
Only a Constitutional amendment can change the designation of the District of Columbia in order to be eligible to be a state.
ETA... and before being allowed to become a state, the land would have to be returned to the original state(s) of Maryland and Virginia.