The US offered to buy Mexican land
The United States did offer to buy Mexican land on multiple occasions throughout history. One significant example is the Treaty of Guadalupe Hidalgo, signed in 1848, which ended the Mexican-American War. Under this treaty, Mexico ceded a significant portion of its territory, including present-day California, Nevada, Utah, Arizona, New Mexico, Colorado, Wyoming, and parts of Texas, Oklahoma, Kansas, and Nebraska, to the United States in exchange for $15 million.
Another proposal to buy Mexican land was put forward during the 1853 Gadsden Purchase. This agreement allowed the United States to acquire additional land from Mexico, mainly in present-day southern Arizona and New Mexico, for $10 million.
Both of these instances highlight instances where the United States actively sought to purchase Mexican land, ultimately resulting in significant territorial acquisitions and border changes between the two countries.