Another to be freed is Ahmed Sadat, secretary-general of the Popular Front for the Liberation of Palestine, incarcerated in Israel for his role in the assassination of Israeli Tourism Minister Rehavam Zeevi in 2001, the report said.
There had been no official Israeli response to the report but in past prisoner deals Israel has refused to release Barghouti and Sadat.
U.S. Ambassador to Israel Dan Shapiro informed Palestinian President Mahmoud Abbas of the move in a telephone conversation, the Palestinian official said.
The prisoners' release is expected to occur prior to Obama's arrival in Israel next month, the newspaper said.
Barghouti's wife, Padwa, wrote on her Facebook page that talks are under way for her husband's release, the report said.
But Nimer Hamad, Abbas' political adviser, said Israel would not release Barghouti and Sadat.
Ziad Abu Ein, head of the Palestinian Authority's prisoners release bureau, said Washington is placing pressure on Israel to renew negotiations with the Palestinians.
The Palestinians are waiting for Israel's response on the renewal of peace talks and its agreement to halt all construction in West Bank settlements, he said.
Obama is to spend two days in the region. During part of his visit he'll be in Ramallah meeting Abbas and other Palestinian officials, the newspaper said.