N.M. Stat. § 13-1-131
An invitation for bids, a request for proposals or any other solicitation may be canceled or any or all bids or proposals may be rejected in whole or in part when it is in the best interest of the state agency or a local public body. A determination containing the reasons for cancellation shall be made part of the procurement file. If no bids are received or if all bids received are rejected and if the invitation for bid was for any tangible personal property, construction or service, then new invitations for bids shall be requested. If upon rebidding the tangible personal property, construction or services, the bids received are unacceptable, or if no bids are secured, the central purchasing office may purchase the tangible personal property, construction or services in the open market at the best obtainable price.
NMS § 13-1-131