Abbas had agreed to engage in indirect peace talks with the Israelis only after obtaining official support from the PLO's leadership and the Arab League, which endorsed the launch of indirect talks last week.
If the PLO approves the talks, Mitchell is expected to officially announce later on Saturday or Sunday that talks will begin, US and Palestinian officials said.
Al Jazeera's Nour Odeh, reporting from Ramallah, said there is a lot of opposition to the idea of going back to talks.
"Many factions, including senior figures in the Fatah movement, believe that the conditions on the ground are not appropriate for negotiations to go ahead and yield positive results," she said.
"Still, the Palestinian president is expected to push hard for that endorsement because there are some in the Fatah leadership who believe this is a chance the Palestinians should be giving to the American administration.
"There is no faith in the Israeli partner."
The talks also faced opposition in the Gaza Strip, where Hamas, the Palestinian group which governs the Palestinian enclave, called on the PLO to reject the resumption of talks, dismissing them as "absurd".
"We warn the executive of PLO not to take any decision to resume talks with the enemy and to give cover to the Israeli occupation to commit more crimes against our people," Hamas said in a statement.
Khalil Shaheen, a political analyst in the West Bank, said the Palestinian people do not consider the meeting representative of all Palestinians.
"Take into consideration that Hamas is not a member of the PLO and we have some factions on the left that are against and reject direct or indirect negotiations," he told Al Jazeera.
"For the Palestinians, they are more concerned about the coming change in [the Palestinian] government more than they are concerned about negotiations that will not bring them any breakthrough towards establishing their own Palestinian state."
Negotiations between the Palestinians and Israel have been stalled since Israel's three-week assault on the Gaza Strip began in December 2008.
Attempts to restart the stalled process last month collapsed when Israel announced construction of a new housing project in occupied East Jerusalem, which Palestinians see as the future capital of any independent state.
The talks will not be the face-to-face meetings the administration of Barack Obama, the US president, had hoped to put in place, but will involve US officials meeting with one side at a time.
Mitchell has been shuttling between Israeli and Palestinian leaders in a bid to relaunch the dialogue.
He met Shimon Peres, the Israeli president, on Friday who said Israel is ready to negotiate with the Palestinians.
"Israel seeks a historic peace agreement with the Palestinians that will result in the founding of an independent Palestinian state alongside Israel," Peres said.
Peres said his country also wants its security concerns addressed in the initial stages of the indirect talks.
He said resolving security concerns, such as rocket fire from the Hamas-controlled Gaza Strip, are of utmost importance to Israel.
The Palestinians, however, have said they want the indirect talks to focus on the final borders of their future state.
Either way, Abbas has said that the talks will not last longer than four months. He said earlier this week that he would consult the Arab League for advice at the end of the four-month period.
Binyamin Netanyahu, the Israeli prime minister, announced a 10-month settlement freeze in the West Bank in November.
Abbas' timetable for indirect talks will roughly coincide with the end of that freeze.
Israeli officials have said repeatedly that they won't approve another halt in construction, regardless of what happens during negotiations.