"It has always been my dream to come back home and play," Peterson said. "Taken that I've been living in Houston for over a decade. That would be a perfect landing spot, here in my backyard. That would be very convenient."
Peterson is from Palestine, Texas, which is less than three hours from Houston.
The veteran running back was released by the Arizona Cardinals earlier in the week before he would have been owed a $750,000 bonus. Peterson played six games for the Cardinals last season and four for the New Orleans Saints to start the year.
Peterson injured his neck in Week 12 and did not play the rest of the season, but he told ESPN's Josina Anderson on Monday that the Cardinals' doctor told him that his "neck is completely healed" after reviewing his scans.
Peterson, who turns 33 next week, said Friday that he knows he has "at least three to four" years left in the NFL and that "as far as my body and how I feel physically, I feel great."
Last January, Peterson went on First Take and mentioned that "Houston would be a good spot" for him to play if he did not re-sign with the Minnesota Vikings. A team source later told ESPN that the interest was all generated by Peterson, and the Texans "never once talked about him."
"It has always been my dream to come back home and play." Adrian Peterson
The Texans are not necessarily in need of a veteran running back; Lamar Miller is in his third season in Houston and the team drafted D'Onta Foreman in the third round of the 2017 NFL draft. Although Miller is coming off of his worst NFL season, Foreman looked promising before he tore his Achilles at the end of November.
Still, Peterson said he felt he stood out during a joint practice between the Saints and Texans last year and showed he could make a difference in Houston's running back room. "[The Texans are a] great organization to be a part of," Peterson said. "Great defense, Watson at the quarterback position, some great young receivers. I've been watching the last couple of years, so I've seen the pieces they've added to get to where they are now.
"I feel like personally, when I look at the team, I feel like I could add to that running back room and really make a good running game dominant."