While it's often overshadowed by the later conflict, the US had actually been trying to buy Texas since the 1820s. When the Adams-Onis Treaty was signed in 1819, there were a lot of American expansionists who felt that the US had effectively ceded Texas to the Spanish by accepting the Sabine as the border. That feeling was based on old French claims that Texas was part of Louisiana, which while shaky contained enough truth to sustain the argument.
After achieving independence, Mexico struggled to protect and govern Texas, which fed into American perceptions that they might be willing to part with it to shore up their financial situation. Unfortunately for the Americans, their choice in ministers to Mexico was extremely poor. James Wilkinson was a corrupt and conniving man, who actually undermined the negotiations because he had a financial stake in Mexican Texas. He would die and be replaced by Joel Roberts Poinsett in 1825, who had already spent a few years in Mexico by that time. Poinsett was a smart and well travelled man, a certain upgrade over Wilkinson, but he couldn't resist interfering in Mexican politics. Specifically he promoted Yorkist freemasonry, which aligned itself with American style republicanism and liberalism. Mexico would ask that Poinsett be recalled, which happened in 1829. His meddling created a perception within Mexican political circles that the American interest in Texas was intertwined with a desire to undermine Mexico's political stability.
Unrelated but poorly timed, in 1826 the empresario Haden Edwards got in trouble for corrupt activities in Texas and the Mexican authorities attempted to capture him. Rather than surrender, he formed a posse and declared independence for eastern Texas, calling it the Republic of Fredonia. There wasn't much substance to the rebellion and he fled to Louisiana the following year to avoid the Mexican army. The whole affair was fairly trivial, Edwards having received very little support from his fellow Texians, but it seemed to confirm Mexican fears that Americans were actively attempting to undermine Mexico and peel Texas away.
While all that might point to the Americans having poisoned the well, the Mexicans can also be blamed for having poorly managed and responded to the situation in Texas. Since the late 18th century, the Spanish had maintained a fragile peace with the Comanche, through a mix of military intimidation and gifts. However, Mexico's war of independence left it poor and exhausted, unable to continue those policies. It chose instead to invite Americans into Texas as a means of settling and protecting the territory, so that Mexico City might turn its attention to more important matters. The 1820s saw a flood of American settlers, many of them looking for a fresh start following the Panic of 1819. By the end of the decade Americans formed a solid majority within the territory. Initially the Mexican government took a laissez faire approach to the Americans settlers, but the Fredonian rebellion triggered crackdowns starting in 1828. Edward's actions had been largely condemned by the rest of the Americans settlers, which created a perception that Mexico was unfairly punishing them as a whole for the crimes of a few. Inadvertently the Mexicans had planted the seeds for a revolt in Texas through their efforts to prevent one.
In the late 1820s and early 1830s, Mexico's political situation became much more volatile and polarized. The revolving door of leadership created uncertainty, both domestically and abroad. Mexico's peripheral territories, including Texas, became worried that their status and rights might change at any moment. For the Americans, this instability meant that they could simply wait for one uncooperative administration to fall before restarting talks with the next. During those tumultuous years, anti-Americanism was one of few unifying principles in Mexican politics, so compromising on Texas was a political landmine that few were willing to step on. Ironically, it was that same view on Texas that made the Mexican government reluctant to militarily intervene in the territory, as it was seen as major political prize for whoever could pacify it. Santa Anna would attempt to claim that honor in 1836, but we all know how that turned out.
My reason for explaining all this is to show why it would've been extremely hard for the Americans to negotiate this purchase in 1845 without some degree of coercion. By that point Mexican goodwill towards both Texas and the United States was almost nonexistent for numerous reasons. To make any purchase possible, you'd likely have to keep Poinsett out of Mexico and butterfly away Edward's rebellion in 1826. From there I suspect you'd have a decade or two of decent relations. If during that time Mexico's instability continues and it sees the financial necessity, it might be willing and politically capable of parting with some of its northern territory. I suspect this would probably be a smaller exchange that what we saw in OTL. Eastern Texas would be the main goal, probably defined at either the (Texan) Colorado or Nueces rivers. Northern California is probably also a target of American negotiations, with eyes on the port of San Francisco, so they probably look for a border somewhere between the 33rd and 37th parallels. Frankly this is a favorable outcome for Mexico in comparison to OTL, as it eases some of its administrative strain along with aiding its financial situation, not to mention avoiding two costly and humiliating wars and the loss of all the territory that came with that.
