Prince Bandar bin Sultan told European diplomats that Washington had failed to act effectively on the Syrian crisis and the Israeli-Palestinian conflict, was growing closer to Tehran, and had failed to back Saudi support for Bahrain when it crushed an anti-government revolt in 2011, the source said on Tuesday.
It was not immediately clear if Prince Bandar's reported statements had the full backing of King Abdullah.
"The shift away from the US is a major one," the source close to Saudi policy said. "Saudi doesn't want to find itself any longer in a situation where it is dependent."
"This happens after the US failed to take any effective action on Syria and Palestine.
"Relations with the US have been deteriorating for a while, as Saudi feels that the US is growing closer with Iran and the US also failed to support Saudi during the Bahrain uprising."
UN seat rejection
The prince's initiative follows a surprise Saudi decision on Friday to reject a coveted two-year term on the UN Security Council in protest at "double standards" at the United Nations.
John Kerry, the US secretary of state, said he had discussed Riyadh's concerns when he met his Saudi counterpart, Saud al-Faisal, in Paris on Monday.
Kerry said he had told the Saudi minister that no deal with Iran was better than a bad deal.
"I have great confidence that the United States and Saudi Arabia will continue to be the close and important friends and allies that we have been," he told reporters in London.
"I reaffirmed President Obama's commitment that he will not allow Iran to have a nuclear weapon," said Kerry.
Prince Bandar, who was Saudi ambassador to Washington for 22 years, is seen as a foreign policy hawk, especially on Iran.
The kingdom has informed the US of its actions in Syria, and diplomats say it has respected US requests not to supply the groups with advanced weaponry that the West fears could fall into the hands of al Qaeda-aligned groups.
Saudi anger boiled over after Washington refrained from military strikes in response to a poison gas attack in Damascus in August when the Syrian president, Bashar al-Assad, agreed to give up his chemical arsenal.
Saudi Arabia is also concerned about signs of a tentative reconciliation between Washington and Tehran, something Riyadh fears may lead to a "grand bargain" on the Iranian nuclear programme that would leave it at a disadvantage.