She and EU president Donald Tusk on Thursday held their first face-to-face talks since she triggered the process for leaving the bloc as Brexit negotiations loom.
The visit follows an outcry in Britain over Tusk last week outlining draft negotiating guidelines which say that Spain should have a veto on any trade deal agreed with Britain being extended to Gibraltar.
And it comes a day after the European Parliament approved a series of Brexit demands, including calling for "substantial progress" to be made on an exit deal before talks on future trade relations can begin.
"I'll be talking with president Tusk about how we can ensure, within the timescale we have got, that we can deliver a deal," May said ahead of the meeting.
A European Union source told AFP that the meeting was "not part of the negotiations" but would be "a first opportunity for Tusk to explain his draft Brexit guidelines to be adopted on April 29".
EU leaders are holding a special summit in Brussels on that date to decide a negotiation strategy.
The actual talks on Britain leaving the EU are not expected to start until May at the earliest.
Britain last week formally notified the EU of its intention to quit the bloc -- the first member state ever to do so -- following a shock referendum vote on June 23 last year in favour of leaving.
When announcing Britain's intention to leave the EU, May called for the divorce and future trade deal talks to proceed in tandem, but she was rebuffed by Tusk who said that there should first be progress on the exit agreement before trade negotiations can begin.
Asked about this divergence of views on the timing of the negotiations during her trip to Jordan and Saudi Arabia this week, May hinted at a compromise.
"Let's look at the whole question of where we end up. At the end of this negotiation, will we have looked at both withdrawal and the future relationship? That's what's important," she said.
May also suggested she could envisage free movement of EU nationals into Britain continuing during a transition period even after the country's expected departure from the bloc in March 2019.
Asked about this possibility, she told Sky News television: "Once we've got the deal, once we've agreed what the new relationship will be for the future, it will be necessary for there to be a period of time when businesses and governments are adjusting systems and so forth," she said.
That led to criticism from the pro-Brexit Leave.eu campaign group, which accused May of "backtracking".
It published a mocked-up image of May alongside a crowd of migrants reading: "We're going to take back control of our borders... Eventually".
Cutting down on the hundreds of thousands of EU citizens who move to Britain every year was one of the main arguments in the referendum campaign.