Trump's remarks represent the first time he has acknowledged an American proposal is with Tehran after multiple rounds of negotiations between US Middle East envoy Steve Witkoff and Iranian foreign minister Abbas Araghchi.
Negotiations have reached the "expert" level - meaning the two sides are trying to see if they can reach agreements on details of any possible deal.
Trump made the comment aboard Air Force One as he ended his trip to the United Arab Emirates, the last stop on his three-nation tour of the Middle East.
"They have a proposal," Trump said on Friday.
"But most importantly, they know they have to move quickly, or something bad is going to happen."
Trump did not elaborate on the substance of the proposal and Iran did not immediately acknowledge having it.
On Thursday, Araghchi spoke to journalists at the Tehran International Book Fair and said that Iran did not have any proposal from the Americans yet.
Araghchi also criticised what he called conflicting and inconsistent statements from the Trump administration, describing them as either a sign of disarray in Washington or a calculated negotiation strategy.
"We are hearing many contradictory statements from the United States - from Washington, from the president, and from the new administration," Araghchi said.
"Sometimes we hear two or three different positions in a single day."
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