The former Heisman Trophy winner was himself subbing for injured first-string signal-caller Matt Schaub when he sustained the broken shoulder in Sunday's game against Jacksonville.
Leinart landed on the shoulder after taking a hit from Jaguars defensive end Jeremy Mincey. Rookie T.J Yates stepped in and led AFC South-leading Houston (8-3) to a 20-13 win.
Kubiak said he is focused on Yates and former New York Jet Kellen Clemens as his quarterback options, but added, "We will bring another guy in. When that will happen, I don't know."
He also refused to rule out an acquisition such as the now-retired Brett Favre.
"I don't think you rule out anybody," Kubiak said. "I know there are a lot of guys being mentioned. I'm not going to rule out anybody nor confirm anybody."
Exploding whale video goes viral on Internet
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'