He is expected to discuss the issue of political prisoners with Ms Suu Kyi, who was released from house arrest in November 2010, BBC reports.
He will also meet other dissidents and representatives of ethnic minority groups seeking greater autonomy.
William Hague, the first British foreign minister to visit Burma in over half a century, had dinner with Suu Kyi yesterday ahead of formal talks after he met senior members of the nominally-civilian government.
Hague urged "further progress" towards human rights and political freedoms after a meeting with President Thein Sein, who has overseen a number of promising steps since taking power in March.
Burma has played host to a series of top international envoys in recent months after controversial 2010 elections heralded the end of decades of direct military rule.
Suu Kyi, who has grown cautiously positive about Burma's future recently, said she expected to live to see a "full democratic election" in Burma, in comments to the BBC before her dinner meeting with Hague.
The Nobel laureate is on course to run in April 1 by-elections after her National League for Democracy (NLD) was officially allowed to register as a political party on Thursday.
Suu Kyi, who was freed from seven straight years of house arrest days after a November 2010 election, could be propelled into parliament by the upcoming poll, although the majority held by the army and ruling military-backed party will not be threatened.
Since taking office last year Thein Sein -- himself a former junta general -- has surprised observers by holding talks with Suu Kyi, suspending an unpopular Chinese-backed dam project and indicating a desire to reach out to the international community.
Some political prisoners have also been released but the government this week caused disappointment when it announced reduced jail terms for inmates but failed to issue a much-anticipated amnesty for detained dissidents.
Hague's trip, the first by a European Union foreign minister since the new government took power, is the latest round of international diplomacy aimed at urging on the budding reforms.
"I made clear that the British government stands ready to respond positively to evidence of further progress towards that lasting improvement in human rights and political freedom that the people of Burma seek," he said in a UK Missions statement following talks with the president.
Hague's visit echoes that of US Secretary of State Hillary Clinton, who met Thein Sein and Suu Kyi during a trip to Myamar at the end of last year.
British International Development Secretary Andrew Mitchell travelled to the country in November and Japanese Foreign Minister Koichiro Gemba visited in December.
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