Ahead of their Champions League clash with Borussia Monchengladbach, Zinchenko was not shy in offering up that City have eyes on lifting all four major trophies over the next two months.
"We have an unbelievable squad, the best players in the world and definitely, why not?" Zinchenko said.
"Inside the dressing room or inside the team I can see the hungry eyes, everyone is so hungry for the titles and that is what you want.
"This period right now I would say is the most important two months in our careers."
Guardiola then sat in front of the media and disagreed with Zinchenko, telling the 24-year-old to concentrate on progressing beyond Gladbach and reach the quarter-finals.
"I am older than Mr Zinchenko. I have more experience. I don't agree with him," Guardiola said. "The only thing Zinchenko has to be worried about is to win tomorrow and go through.
"Four trophies has never happened [in England] and the reality is I don't think it's going to happen. Do I agree with Zinchenko? I would say no. They have to handle the pressure."
Zinchenko added that City owe it to Sergio Aguero and Fernandinho to lift the Champions League as both enter the final months of their contracts.
"They have been here around 10 years each, they deserve," the Ukraine international said. "We are going to try [for them]. Sergio is a living legend.
"We have got an unbelievable squad, everyone deserves to play and you are just waiting for your chance and to deserve to play another game. We are just pushing each other. It is like extra motivation. We just move each other forward."