N.M. Stat. § 19-7-49
Every grazing lessee who desires a new lease on the same lands for a term not exceeding five years shall make and file with the commissioner his application for such new lease on or before August 1st next preceding the expiration of his existing lease; and any and all other applicants for a like lease on such land shall make and file with the commissioner their applications on or before September 1st next preceding the expiration date of such existing lease. If more than one such application to lease be filed as herein provided, one of which shall be that of the holder of the existing lease, the commissioner shall lease such land to the bona fide applicant offering the highest annual rental therefor, if to anyone; except that the commissioner, before so doing, if another bona fide applicant shall offer a higher rental than that offered by the holder of the existing lease, shall give written notice to the holder of the existing lease, immediately after September 1st next preceding the expiration of such lease, of the name and address of the applicant offering the highest annual rental and the amount of such offer, and if the holder of the existing lease, on or before September 30th next ensuing, shall meet such offer and has, in good faith, complied with all the requirements of his existing lease, the lease shall be awarded to him, if to anyone.
NMS § 19-7-49