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."
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged