Since taking the starting spot from Matt Schaub in week seven at the Kansas City Chiefs, Keenum has thrown for 822 yards and seven touchdowns, without any interceptions.
However, Kubiak has stated hat Keenum must carry on in this vein if he is to remain first choice.
Kubiak told the Houston Chronicle: "Case has played really well and done a lot of good things. But he has made a lot of mistakes too which he has to correct.
"He needs pressure on him to play well to stay in there because Matt is working really hard and wants to get back on that field. Nobody is guaranteed anything; much less the quarterback."
It is thought that Keenum will line up against the Oakland Raiders on Sunday.