Theresa May is set to discuss a post-Brexit trade deal with Turkey during weekend talks in the country with President Recep Tayyip Erdogan.
The prime minister arrived in Ankara from the US, where she met President Trump.
A new trading relationship with Turkey following the UK's exit from the European Union would form part of discussions, Number 10 said.
The PM is also expected to discuss security, Mrs May's spokeswoman said.
The spokeswoman added: "They will be discussing a new trade relationship [and] a strategic security partnership."
It comes as Brexit Secretary David Davis predicted a "round of global trade deals" would be "fully negotiated" within 12 to 24 months, coming into force when the UK leaves the EU.
The government plans to begin the formal two-year Brexit process by triggering Article 50 by the end of March.
Both Ankara and London find themselves in a position where they need friends. Many fear that Turkey – a key Nato ally – is heading towards a more authoritarian future under President Erdogan.
He is clamping down on dissent and press freedom, pushing his country further away from the prospect of EU membership and in the process drawing strong criticism from European governments.
Mrs May arrives as an advocate of "global Britain" – this policy a necessity following the Brexit decision.
The UK has a strong security relationship with Turkey – an ally in the fight against so-called Islamic State (IS) – and she will also be seeking preliminary understandings on bilateral trade.
But she will need to show her domestic critics that the growing emphasis on trade in Britain's relationships abroad does not come at the expense of values such as human rights.
Mrs May's first prime ministerial visit to Turkey comes as President Erdogan is increasing pressure on opponents following the failed military coup in July 2016.
Asked whether Mrs May would raise human rights concerns since the coup, the spokeswoman said Britain had "expressed our strong support for Turkey's democracy and institutions following the coup".
In further unrest, 39 people were killed in an attack on a New Year's Eve party at a nightclub in Istanbul.
IS said it was behind the attack and the militant group was linked to at least two other attacks in Turkey last year.