The newspaper cites unnamed senior officials at the White House, the Foreign Ministry, and the Pentagon.
No agreement is imminent, said one of the officials.
I'm not sure it will ever happen.
The White House has previously stated that Israel and Hamas have already agreed to "90 percent" of the proposed agreement and that hope for a breakthrough remains.
The pessimism mainly concerns two things, writes WSJ. Firstly, the number of Palestinian prisoners that Israel must release in exchange for hostages, and secondly, the threat of full-scale war between Israel and Hezbollah following last week's electronic attacks in Lebanon.
The White House spokesperson Sabrina Singh had a more optimistic message on Thursday, before publication:
I can say that we don't think this agreement will collapse, she told reporters.
The Biden administration has been trying for months to reach an agreement on a ceasefire in Gaza and a hostage exchange between Israel and Hamas. Both sides frequently accuse each other of not really wanting to come to an agreement.