The officials say the appearance of two of the Americans on Iranian television this week was "part of the process."
A U.S. State Department spokesman said he was unaware of any deal but said, "I hope it is true."
Earlier this week, the State Department said it was "appalled at the mistreatment" of the two Americans who were "paraded" on state-run television.
Like almost every dealing between the U.S. and Iran, this one touches on the sensitive and volatile issue of nuclear weapons and sanctions.
The U.S. officials told ABCNews.com that a European country is brokering the deal, which they say Iran hopes will help delay a third set of sanctions being considered by the United Nations Security Council over Iran's refusal to halt its nuclear program.
Three of the Americans are being held in an Iranian prison and a fourth, Parnaz Azima, of the U.S.-funded Radio Farda, has been released on a $50,000 bail.
Iran has previously admitted holding Haleh Esfandiari, of the Washington-based Woodrow Wilson Center; Ali Shakeri, a California businessman; and Kian Tajbakhsh, a consultant for the Soros Open Society Institute.
The officials say a fifth American, former FBI agent Robert Levinson, is not part of the deal. Levinson disappeared in Iran in March. U.S. officials believe he is in a Tehran prison although Iran has never acknowledged he is in custody.