“I believe it is profoundly in all our interests for the negotiations to succeed but I know that some are worried whether we are prepared in the event that they do not. It is our responsibility as a government to prepare for every eventuality," May told her Conservative Party's annual conference in Manchester on Wednesday.
"I know some find the negotiations frustrating," she said, adding: "But if we approach them in the right spirit... I am confident we will find a deal that works for Britain and for Europe too".
May also said she understood EU citizens living in Britain who felt "unsettled and nervous".
"Let me be clear that we value the contribution you make to the life of our country. You are welcome here and I urge the negotiating teams to reach agreement on this quickly because we want you to stay," she said.
The prime minister was speaking at the close of the party’s four-day conference, a day after the European Parliament overwhelmingly voted for a measure calling for trade talks between the EU and UK to be delayed because Brexit talks have not made sufficient progress.
Members of the European Parliament meeting in Strasbourg, France, condemned May's government on Tuesday, saying infighting in her cabinet was hindering talks on key exit issues including Britain's divorce bill.
Senior leaders in Brussels said on Tuesday that the talks regarding Britain's exit from the EU had failed to make "sufficient progress" to justify discussing a post-Brexit free trade relationship with London.
May's authority was severely weakened by the snap election in June and her cabinet remains divided over Brexit, even as negotiations in Brussels move slowly forward.
May used her speech in Florence, Italy, last month to offer a number of concessions to Brussels in a bid to unlock the Brexit talks.
In her speech, she stressed that the UK would leave the European Single Market, but noted that London still wanted economic relations with the bloc and it will not turn its back on Europe.