Gulbadin is considered to be one of Afghanistan's most wanted men and has sent his son, Feroz, to represent him at the meeting.
"What we understand is that they are trying to forge unity among themselves," the source said.
Mohammed Nasheed, the Maldivian president, said in a statement it had helped
with the gathering in the interest of peace in the region.
"Afghanistan's stability affects the peace and security of our region. The government of Maldives supports efforts to bring a resolution to the conflict in Afghanistan," Nasheed's press secretary said.
Al Jazeera's Dan Nolan, reporting from the island, said that Western officials had been deliberately excluded from the process.
"There are no international observers here. The people organising these talks say these are Afghan problems that need Afghan solutions".
The meeting is the second such gathering held in the Maldives and it comes ahead of a grand assembly, or "jirga", of Afghan tribal and community leaders, called by Hamid Karzai, the Afghan president, scheduled for the end of May.
Thousands of people are expected to attend the jirga to discuss the main issues facing the fractious country in the context of Karzai's plans to bring peace and development after more than eight years of war.
His plan calls for the removal of names of certain Taliban leaders from a UN blacklist and possibly giving them asylum in another Islamic country from where they can engage in talks with the Afghan government.
The US state department said it was aware of the Maldives talks.
"We continue to support efforts by the Afghan government to open the door to those Taliban who abandon violence and respect human rights of their fellow citizens," P.J.
Crowley, the US state department spokesman, said.
"We are not saying they are a good thing or a bad thing. The real question is, what comes out of this."
In January, Al Jazeera revealed that a secret meeting between government and Taliban officials had taken place on the Indian Ocean islands as part of an effort to engage the Taliban in the political process.
The Maldives may seem an unlikely location for a meeting of this type, but the popular tourist destination is used to host the talks because it is one of few countries that issues visas to Afghans on arrival.
Many of the participants would risk arrest if they attended such a meeting in Afghanistan.
Afghanistan is mired in a war with Taliban-led anti-government fighters, with the 130,000 Nato and US troops due to rise to 150,000 by August.