Appearing on NFL Network, Houston Chronicle columnist John McClain said he believes Shaw will be a prime candidate to replace Kubiak in Houston.
"There's going to be a lot of candidates," McClain said. "Shaw has an NFL background, NFL pedigree. He could leave Stanford for just about any job he wanted, but the Texans, I know, will check him out as well as Lovie Smith and some others.
"I think the fact they want someone with an NFL background is very telltale," he said. "That rules out college head coaches that have never been in the NFL."
Shaw has had stints as an NFL assistant coach for the Philadelphia Eagles, Oakland Raiders and most recently the Baltimore Ravens. He was the offensive coordinator at Stanford from 2007-10 under Jim Harbaugh, now head coach of the San Francisco 49ers, before taking over as the Cardinals' head coach in 2011. Stanford has gone 33-6 under Shaw, including a 10-2 record this year.
Stanford meets Arizona State on Saturday in the Pac-12 championship game.
Earlier this season, Shaw was mentioned as a possible candidate for head coaching jobs at USC as well as Texas. He denied having interest in both jobs.