Trade and Industry Minister Maqbul bin Ali said there would be negotiations with the US in March and April although the US Embassy in Muscat refused to confirm an agreement had been made on Tuesday.
The accord is likely to cause friction with Saudi Arabia, Oman's northern neighbour, which is opposed to fellow member states of the Gulf Cooperation Council making bilateral agreements with the United States.
The agreement will become effective in 2006 if it is approved by the US Congress, Bin Ali told a meeting of Omani business executives.
The minister added that a US delegation will visit Oman between 12-14 March to discuss the accord and an Omani delegation will hold talks in Washington on 18 April.
Last year Bahrain signed a free trade agreement with the US.
Saudi Arabia complained that such accords weakened the collective bargaining power of the Gulf Cooperation Council, a loose political and economic alliance that groups Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates.
The Saudi government downgraded its representation at the GCC summit in December in a move widely seen as reflecting Saudi disapproval of Bahrain's pact with Washington.
A third member of the GCC, the United Arab Emirates is negotiating for a free trade accord with the US.