Netanyahu, set to travel to Washington next week for direct talks, intends to handle the negotiations personally, the source said, speaking on condition of anonymity.
Chief Palestinian negotiator Saeb Erekat said of Netanyahu's plan, It is premature to talk about this now.
The proposal had been passed on to Washington, where the two leaders are due to attend a dinner with U.S. President Barack Obama on September 1.
Abbas and Netanyahu will start negotiations the following day after months of indirect contacts. There remains deep scepticism about whether they can reach a deal.
U.S. Secretary of State Hillary Clinton said the United States believed all major issues could be resolved within a year. But Netanyahu's own foreign minister said there was virtually no chance of reaching a deal in that time.
The negotiations could stumble as soon as September 26, when a 10-month limited Israeli moratorium on new housing starts in Jewish settlements in the occupied West Bank expires.
Abbas, whose authority has been limited to the West Bank since Hamas Islamists took control of the Gaza Strip in 2007, has threatened to pull out of the talks if Israel presses ahead with settlement construction.
CALM & CONTINUOUS NEGOTIATIONS
The United States opposes settlement expansion but has stopped short of calling for Netanyahu to extend the moratorium, a move that could cause cracks in his governing coalition dominated by pro-settler parties including his own.
Instead, it has urged both Israel and the Palestinians not to take measures that could jeopardise the negotiations and said the settlement issue would be raised in next week's talks.
Under Netanyahu's proposal, he and Abbas would meet once every two weeks to try to reach quiet understandings on the key issues, and afterwards the two teams will discuss the details, the diplomatic source said.
The source said Netanyahu had chosen a small team of advisers with attorney Yitzhak Molcho as chief negotiator.
Israeli and Palestinian officials said White House envoys David Hale and Daniel Shapiro met separately with Molcho and Erekat to lay the groundwork for the summit.
They briefed us on issues for the talks and preparations for the meeting in Washington, Erekat told Reuters.
An Israeli official earlier quoted Netanyahu as saying, The only serious negotiations in the Middle East are direct negotiations, calm and continuous, between the leaders on the fundamental subjects.
A similar formula was used in peace negotiations between Netanyahu's predecessor, Ehud Olmert, and Abbas, who in a series of meetings talked privately every few weeks.
The Olmert-Abbas talks, launched at a conference in 2007 -- also in the United States, came close to producing a final deal, both leaders said at the time.
But the negotiations faltered when the scandal-plagued Olmert was forced to resign. They collapsed after Israel launched an offensive in the Gaza Strip in late 2008.
Many of the meetings were at Olmert's official residence, but Olmert also became the first Israeli premier to travel to the West Bank since 2000, meeting Abbas in Jericho.
(Additional reporting by Mohammed Assadi; Editing by Louise Ireland)