Culley's firing came on Thursday, days after Houston finished with a 4-13 season, losing 28-25 to the Tennessee Titans, the AFC's top playoff seed.
Four days earlier, on Monday, 66-year-old Culley had said that he expected to return for a second season with the team.
That same day, the Miami Dolphins fired head coach Brian Flores, who is now believed to be targeted by the Texans.
Texans are targeting former Dolphins coach Brian Flores as their top candidate at this time, according to multiple league sources. He has a strong relationship with Nick Caserio.— Aaron Wilson (@AaronWilson_NFL) January 13, 2022
Citing league sources, the NFL's Aaron Wilson said Flores is considered a top candidate who has a strong relationship with Texans general manager Nick Caserio.
Flores spent 11 seasons as an assistant coach with the New England Patriots, including as a linebackers coach. He called defensive plays for the team in 2018.
Hiring Flores would be far from the Texans' only tie to the Patriots.
ORIGINAL STORY: Texans fire head coach David Culley after going 4-13 in his debut season
Both Caserio and Jack Easterby, executive vice president of football operations, both came from the organization, with the former spending two decades with the Patriots.
But someone else is considered a leading candidate, and that's Jerod Mayo.
ESPN's Adam Schefter reported after Culley's firing that Mayo, the current Patriots' linebackers coach, is expected to emerge as the leading candidate for the vacant Texans position.
Mayo used to play for New England and retired in 2016. He re-joined the organization as an assistant coach in 2019.
On Friday morning, Caserio addressed the media for the first time since the team announced it would be moving on from Culley, who at the time of his hire, was the oldest first-time NFL head coach.
"Ultimately, that was the position that I've been placed in by the McNair family, to do the right thing for the organization," he began.
Caserio said the organization was in a "rough spot" when he took over in January 2021, but added that it's in a better position now.
"We're in a lot better position, and quite frankly, I think that's because of the leadership and the guidance and the direction that David Culley provided this football team," he explained.
Caserio described the decision to fire Culley as "difficult" but "never personal."
"In the end, this is my decision, this is something that I felt we needed to do that was in the best interest of the organization," he said.
Culley had signed a five-year deal to take over the struggling franchise in a move that Caserio explained as being "the best fit for the Houston Texans organization at the time."
When Culley was fired, Caserio said "philosophical differences" were among the reasons he was let go, but didn't elaborate on specifically what those things were.
"There are some things that we did OK, and there are some other areas, quite frankly, that weren't good enough," Caserio started. "I would say all of us need to be better. I certainly need to be better. There might be some things that I can do to help whoever that coach is and maybe I could have done a better job to help David with some of those things. Ultimately, I'm going to take accountability and responsibility."
#Texans GM Nick Caserio says "philosophical differences" and different "vision(s) for our program moving forward" led to David Culley's firing. Caserio admits a change after one season is unusual.— Greg Bailey (@GregBailey13) January 14, 2022
ABC13's Adam Winkler will have more on Caserio's comments and the search for the next coach on Eyewitness News at 4 p.m. and 6 p.m.
The Associated Press contributed to this report.