"The problem first of all is that we don't have nuclear weapons," Duda told the Gazeta Polska newspaper on Wednesday.
He also said there is "no indication that in the near future", Poland will gain nuclear weapons.
But, Duda added: "There is always a potential opportunity to participate in Nuclear Sharing. We have spoken to American leaders about whether the US is considering such a possibility. The topic is open."
Nuclear sharing is part of Nato's policy of nuclear deterrence, which allows member countries without nuclear weapons to take part in planning for their use by Nato. The weapons are hosted by certain countries but remain under the control of the United States. (PAP)