The King made the private suggestion during a meeting in March last year in Riyadh with John Brennan, the White House counter-terrorism adviser.
But he stated that "keeping track of detainees was an extremely important issue" and promised to review such a suggestion with "appropriate officials" when he returned to the United States.
The remarkable suggestion was contained in a State Department cables summarising the meeting, that was published by Wikileaks and posted on the Guardian's website.
"'I've just thought of something," the King added, and proposed implanting detainees with an electronic chip containing information about them and allowing their movements to be tracked with Bluetooth," the cables said."
"This was done with horses and falcons, the King said.
"Brennan replied 'horses don't have good lawyers' and that such a proposal would face legal hurdles in the U.S, but agreed that keeping track of detainees was an extremely important issue that he would review with appropriate officials when he returned to the United States."
The King of Saudi Arabia also privately urged the United States to attack Iran to destroy its nuclear weapons programme, according to diplomatic cables leaked by the whistle-blowing website,
He told Mr Brennan it was "critically important" for President Obama to "restore America's credibility".
"When asked what advice he had for President Obama, the King said he had 'one request': that it was 'critically important to restore America's credibility' in the world," the cables said.
Mr Brennan reiterated President Obama's commitment to close Guantánamo to "eliminate the potential propaganda benefits its existence provided to al-Qaeda but also because it was the right thing to do".
"Brennan reassured the King, however, that President Obama would remain strong on counterterrorism," the cables added.