Kubo played in Japan's humbling 4-0 thrashing by Chile in their Group C opener in Brazil before coming off the bench in Thursday's 2-2 draw with Uruguay.
The 18-year-old, nicknamed the "Japanese Messi" and who was signed by Real Madrid just before the tournament began, had only made one appearance for the national team before that, in a pre-tournament friendly last month.
"Our aim is to reach the quarter-finals and we're going to decide whether or not we start (Kubo) based on the training session we're about to have," said Moriyasu on Sunday afternoon.
"He has the ability, as you've seen, to play from the start."
Moriyasu, who has brought a mostly under-23 squad to Brazil, gave seven players their debut against Chile.
He recalled a number of experienced campaigners, including Leicester City veteran Shinji Okazaki, for the Uruguay match, but still gave another two players a first cap.
Japan have a simple equation ahead of them for their final Group C encounter: win or go home.
Ecuador are in the exact same boat, while a draw between the teams will knock them both out and see Paraguay qualify as one of the two best third-placed sides along with Peru.
"When we arrived in Brazil we wanted to get a point, a goal in the Copa America," said Moriyasu.
"Now we have those and we want a win... We're going to play to win."
This is Japan's second Copa America participation as invitees.
The first time, in Paraguay in 1999, they lost 3-2 to Peru and 4-0 to the hosts before ending with a 1-1 draw against Bolivia, meaning they are still waiting for a first tournament success.
They are participating alongside fellow Asians Qatar -- who beat them in the AFC Asian Cup final in February.
It's something that has drawn criticism from Paraguay coach Eduardo Berizzo and Venezuela handler Rafael Dudamel.
But Moriyasu refused to be drawn on that controversy.
"I'm not interested in that, it's their opinions. Our players came prepared," he said.
He caused a stir by bringing a largely under-23 squad to the competition -- something that could stand Japan in good stead at the Tokyo Olympics next year in which teams field an under-23 squad that can include up to three older players.
Moriyasu said his hands were tied in that respect having failed to negotiate the release of some of his top players from their clubs.
"Maybe it's not our strongest team but they are the best players that we could bring."
Asked what he would think about Brazil being invited to the AFC Asian Cup one day, Moriyasu said: "If that were the organizers' decision, we would respect it."