Indyk was due to hold talks with chief Palestinian negotiator Saeb Erakat in the West Bank city of Jericho from 1330 IST, the source said, but he had no details of the US-Israeli meeting and Israeli officials did not respond to requests for information.
Yesterday's talks, in a Jerusalem hotel, were "very difficult", the source said.
"The gap...Is still wide."
State Department spokeswoman Jennifer Psaki said this week that Israeli and Palestinian negotiators are striving to reach an agreement to extend their peace talks beyond an April 29 deadline.
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"Kerry keeps them going like a gambler in a casino who insists in putting his money on the roulette wheel, with the hope that the wheel will stop on his number at some point," Barnea wrote.
"He believed that he would reach a peace agreement; then he limited himself to a framework agreement; he later limited himself even further to an American proposal for a framework; and then just to ideas.
Washington is pushing for an extension but the negotiations hit an impasse two weeks ago when Israel refused to release a group of Palestinian prisoners as agreed at last year's launch of the talks.
Under the agreement, Israel had committed to freeing 104 prisoners held since before the 1993 Oslo autonomy accords in four batches, but it cancelled the release of the last group of 26.
Among them are 14 Arab Israelis who the Jewish state is refusing to set free.