Gambari is also expected to meet Aung San Suu Kyi, the detained pro-democracy icon of the country, according to the spokesman of her opposition National League of Democracy (NLD) party.
Suu Kyi had refused to meet Gambari last August in an apparent rebuff of his failed efforts to secure any political reform in the country.
Despite the previous deadlock, Ban Ki-moon, the UN secretary-general, asked Gambari "to continue his consultations with the government and other relevant parties," in the latest trip, Marie Okabe, a UN spokeswoman said.
Myanmar has been ruled by the military since 1962. An election in 1990 saw the NLD win a landslide victory, but the military government refused to allow them to take office.
The government adopted a new constitution in 2008, saying it intends to hold elections in 2010.
However, the forthcoming poll has already been dismissed by the Western critics as a sham because the NLD would not be allowed to participate in the poll.
Human rights groups say that more than 2,100 political prisoners are being held in Myanmar, up sharply from nearly 1,200 before pro-democracy protests were crushed by security forces in September 2007.