On a one-day visit to the Turkish capital, her first since becoming premier, May will hold talks with President Recep Tayyip Erdogan and Prime Minister Binali Yildirim.
While some EU states have been wary of sending top officials to Turkey following the July 15 failed coup and ensuing crackdown, May will follow several senior British ministers who have visited Ankara in recent weeks.
And symbolically, her visit to Turkey is the last leg of a trip which took her to the White House as the first foreign leader to be hosted by Trump.
But following Britain's June vote to leave the bloc, both sides are now looking to bring a new dynamic to relations, with London seeking to firm up post-Brexit trade deals with non-EU states.
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May's spokeswoman said increased security cooperation, especially on aviation, and a new trade relationship post- Brexit would top the agenda at the talks.
Following the failed coup, Turkey's relations with the EU have become strained, with Brussels sharply criticising the extent of the ensuing crackdown, and Ankara deploring Europe's failure to show solidarity.
"The Prime Minister's approach is quite clear - she thinks it's important, and in the UK's national interest - to engage with Turkey on a range of issues - from defence and security cooperation to capitalising on trade opportunities," she said.
She added: "I don't think there are any issues that the prime minister is afraid to bring up."
Ahead of May's visit, Britain's Trade and Investment Minister Mark Price held a series of meetings with Turkish ministers in Ankara.
Three months after the Brexit vote, Foreign Minister Boris Johnson made a colourful visit to Turkey during which he said Britain was seeking a "jumbo free trade deal" with Ankara.