Leinart will be placed on injured reserve after fracturing his left collarbone in the second quarter of Houston's 20-13 win in Jacksonville on Sunday.
The left-handed Leinart was making his first start since 2009 in place of Matt Schaub, who broke a bone in his right foot in the Texans' 37-9 win in Tampa Bay on Nov. 13.
Kubiak says Leinart will have surgery within the next week, and Schaub is due to have surgery on Wednesday to repair a Lisfranc injury.
Kubiak says Houston will try out other quarterbacks this week and hinted the 42-year-old Favre, who retired in January after 20 seasons, could be considered.
"I don't think you rule out anybody," Kubiak said when asked about Favre specifically. "There are a lot of names being mentioned. We've got to continue to work through the process.
"I'm not going to rule out anybody, nor confirm anybody."
Favre's agent, Bus Cook, said late Monday the Texans have not contacted him about Favre.
"I've been a little bit part coach, part counselor here the last couple of weeks," Kubiak said. "I've got Schaub in my office all day last Monday and today I've got Lefty (Leinart) up there. It's just difficult. It's difficult for both of them."
Despite losing one key player after another, Houston (8-3) has won a franchise-record five straight games. Rookie T.J. Yates, a fifth-round draft pick out of North Carolina, will start Sunday's game against Atlanta (7-4). Kellen Clemens, signed last week, will back him up.
Clemens was one of five quarterbacks to try out last Tuesday in the wake of Schaub's injury. Kubiak spent much of Monday discussing all the options.
"When that will happen, I don't know," Kubiak said. "My focus now is strictly with T.J. and Kellen, and moving forward with Atlanta."
Brodie Croyle, Jeff Garcia, Trent Edwards and former Rice quarterback Chase Clement worked out last Tuesday. Clemens had an automatic edge because he spent training camp with the Washington Redskins, where former Kubiak mentor Mike Shanahan and former Texans offensive coordinator Kyle Shanahan are employed.
"I have an opinion on those guys," Kubiak said. "There are some other names that are going to come up in the next day or so. We'll just have to sort it all out."
The 6-foot-3 Yates, a record-setting quarterback for the Tar Heels, went 8 for 15 for 70 yards in place of Leinart on Sunday. Kubiak says he kept the play calls simple for Yates.
"What he had to go do is not easy to do," Kubiak said.
When the Texans drafted Yates, Kubiak compared him to Schaub with his skill set and knack for understanding the game.
He was also attractive to Houston because he ran a similar offense at North Carolina, where he set the school records for yards passing in a career (9,377) and a season (3,418). The Tar Heels' offensive coordinator was John Shoop, who worked on staffs with the Chicago Bears and Oakland Raiders, among other teams.
"He had a lot of things going for him when he stepped in the NFL, as far as how he had been taught," Kubiak said. "He plays the game fast, you have to play fast in this league. You have to be able to get rid of the ball, you have to be able to move.
"He's got those things going for him," Kubiak said. "Now it's just a matter of a ton of reps and we'll see how much progress he can make."
It certainly helps that Yates has the league's best defense and one of its most productive running games supporting him. The Texans gave up only 151 yards in the second half Sunday to preserve their lead.
"Well, the whole group's impressive right now," Kubiak said of the top-ranked defense, yielding 268.4 yards per game. "They're just playing very, very hard. The thing that's most impressive, I use the word 'group' because everybody's making plays. It's contagious."
Houston rushed for only 88 yards in Jacksonville, its second-lowest total of the season, and Kubiak blamed his conservative play-calling for the struggles.
"I don't know if I put our guys in great position," Kubiak said. "I was concerned having one quarterback out there, and making sure that I was trying to find a way to win the game that day. I don't like some of the things I did. We played hard. We just didn't play very good offensively in the second half."