BRUSSELS—As the clock ticks down on the U.K.’s planned departure from the European Union, EU leaders are still waiting for a signal from British Prime Minister Theresa May on the next steps in negotiating a critical divorce deal.

In the meantime, they are losing confidence in her capacity to deliver a majority in her own parliament for any agreement, increasing the chances of a no-deal exit that neither side wants.

One thing European officials say is now certain, although British leaders deny it: If there is a deal, the U.K.’s scheduled departure on March 29 will have to be delayed.

Privately, in Brussels and beyond, European officials say the bloc’s leaders may eventually accept some additions or attachments to the divorce agreement they sealed last November if Mrs. May convinces them Parliament would pass a deal. Both sides are seeking a separation agreement that settles the terms of Britain’s exit and sets up talks on future trade and economic relations.

But those officials now worry that, even if they do make further concessions, Mrs. May still may not be able to drive the deal through her deeply divided legislature.