The Prime Minister will tell MPs that the "ball is in the EU's court" when she updates them on the progress of Brexit negotiations.
"And as we look forward to the next stage, the ball is in their court".
The European Commission's Chief Spokesperson Margaritis Schinas said that the European Parliament's resolution - adopted by nearly all political parties, last week - was clear on sequencing and that they too required the divorce proceedings to take place before plans for a future relationship. "I am sure that we will get a positive response because we are striving to conclude not only the best possible agreement for us but also the best deal for our European friends,".
Chatter concerns whether the final arrangement on citizens' rights can be accorded a status in the United Kingdom similar to the European Communities Act, which gave EU rules supremacy over British law - a legal concept called "direct effect".
Mrs May had tried to reset the deadlocked negotiations by offering to agree to a transition agreement where policy trade policy would remain the same for another two years after we leave in March 2019.
In London, senior officials in May's Conservative party, speaking on condition of anonymity, have urged the prime minister to assert her authority by shaking up her cabinet and firing Foreign Secretary Boris Johnson. European Union officials say there can be no discussion of future trade between Britain and the bloc until there has been "sufficient progress" on divorce terms.
"So I hope our negotiating teams can now reach full agreement quickly", she said.
The European commission's chief spokesman on Monday told reporters in Brussels that there was "clear sequencing" to the talks and "no solution" had been found to move the talks on from the opening withdrawal issues.
Some observers believe it is increasingly likely that May could walk away from the negotiations in part to show she is still in charge of an unruly Tory party.
The debacle intensified debate about whether May can unite her fractious government - divided between Brexit enthusiasts and more reluctant leavers - and how long she can survive as prime minister.
At the Conservative Party Conference, there were concerns about whether she was a strong enough leader to challenge Jeremy Corbyn.
Critics have accused the government of failing to prepare for a "no deal" Brexit, which would mean an end to tariff-free trade with the EU.
The UK will publish papers setting out plans for post-Brexit trade and customs regimes later on Monday, May's spokesman James Slack said. "We should have no fears about a "no deal" scenario".
This week marks the fifth round of negotiations between Britain and the European Union in Brussels. One suggestion, which did not command majority support, was that at the European council summit, the EU would offer to discuss between themselves how a future trade relationship would work or open "scoping" discussions about a transition period, in an attempt to encourage Britain to be more forthcoming.
The fifth round of Brexit negotiations (Article 50) starts today.