The backup quarterback spot is up for grabs.
Brock Osweiler, who signed a free agent deal with the Texans on March 10, is the starter.
Behind him, Tom Savage and DeAndre Hopkins will compete for the understudy's role.
Head coach Bill O'Brien said the competition's "going well" after OTAs, minicamp and the first practice of training camp.
"I thought both of those guys practiced well today," O'Brien said. "We split the team up into two groups for certain drills that we do so that we are able to get a bunch of guys reps, obviously including them, Tom and Brandon."
Savage is the most tenured of the trio in this offense, as he's in year number three with O'Brien and the Texans.
Weeden, meanwhile, was successful in a pair of 2015 contests for the Texans. He came off the bench in place of an injured T.J. Yates to guide Houston to it's first-ever victory in Indianapolis. A week later in Nashville, he started and led the Texans to a win over the Titans.
O'Brien liked what he saw Sunday morning, but wasn't ready to say who would be the backup.
"I thought that they executed well," O'Brien said. "There's no timetable on those types of things as far as who's number two, who's three, all those things. We are just into the first day right now. Those guys just need to keep trying to get better every day."
Weeden completed 26-of-32 pass attempts for 305 yards and three touchdowns. He didn't throw an interception, and also ran for a score in the win at Tennessee.
Savage was on the injured reserve in 2015 after suffering a shoulder injury in the preseason finale last August against the Cowboys.
The second day of training camp is Monday at the Houston Methodist Training Center.
The Houston Texans roster in photos. (Updated 8/2/2021)
TE, Jordan Akins, #88
DL, Auzoyah Alufohai, #98
DB, Cornell Armstrong, #3
TE, Antony Auclair, #83
DL, Ross Blacklock, #90
OL, Justin Britt, #68
DB, Terrence Brooks, #29
TE, Pharaoh Brown, #85
RB, Rex Burkhead, #28
OL, Marcus Cannon, #61
DB, Shyheim Carter, #38
OL, Geron Christian Sr., #72
DL, Maliek Collins, #97
WR, Nico Collins, #12
WR, Chris Conley, #17
WR, Brandin Cooks, #13
WR, Isaiah Coulter, #82
WR, Keke Coutee, #16
DB, Keion Crossen, #35
LB, Zach Cunningham, #41
LB, Tae Davis, #55
QB, Jeff Driskel, #6
DL, Brandon Dunn, #92
WR, Alex Erickson, #14
K, Ka'imi Fairbairn, #7
LS, Mitchell Fraboni, #49
OL, Hjalte Froholdt, #77
OL, Carson Green, #62
LB, Jonathan Greenard, #52
LB, Kamu Grugier-Hill, #51
DB, Vernon Hargreaves III, #26
WR, Damon Hazelton, #86
OL, Charlie Heck, #67
LB, Neville Hewitt, #43
RB, Dontrell Hilliard, #22
OL, Tytus Howard, #71
RB, Buddy Howell, #8
RB, Mark Ingram, #2
OL, Danny Isidora, #73
TE, Ryan Izzo, #81
DL, Jordan Jenkins, #50
RB, David Johnson, #31
DL, Jaleel Johnson, #91
DB, Lonnie Johnson Jr., #1
OL, Roderick Johnson, #63
P, Cameron Johnston, #11
TE, Brevin Jordan, #9
DB, Desmond King II, #25
LB, Christian Kirksey, #58
DL, Shaq Lawson, #93
RB, Phillip Lindsay, #30
DL, Roy Lopez, #79
DL, Jacob Martin, #54
OL, Ryan McCollum, #75
OL, Justin McCray, #64
DL, Whitney Mercilus, #59
WR, Anthony Miller, #18
QB, Davis Mills, #10
DB, Terrance Mitchell, #39
DB, A.J. Moore Jr., #33
WR, Chris Moore, #15
DB, Eric Murray, #23
LB, Hardy Nickerson, #56
DL, Charles Omenihu, #94
DB, Jonathan Owens, #36
RB, Scottie Phillips, #27
LB, Kevin Pierre-Louis, #57
TE, Paul Quessenberry, #45
DB, John Reid, #34
DB, Justin Reid, #20
DL, Derek Rivers, #95
WR, Andre Roberts, #19
DB, Bradley Roby, #21
OL, Max Scharping, #74
DB, Tremon Smith, #24
OL, Jordan Steckler, #70
OL, Lane Taylor, #65
WR, Taywan Taylor, #37
QB, Tyrod Taylor, #5
DL, Vincent Taylor, #96
LB, Joe Thomas, #48
DB, Tavierre Thomas, #42
OL, Cole Toner, #66
OL, Laremy Tunsil, #78
DL, DeMarcus Walker, #44
WR, Jordan Veasy, #84
LB, Garret Wallow, #32
TE, Kahale Warring, #87
QB, Deshaun Watson, #4
LS, Jon Weeks #46
