The source, reportedly on the 10-man leadership council of the group, said: "We got more than $20m from them [the Seoul government].
"The money will also address to some extent the financial difficulties we have had."
But Youssef Ahmadi, a Taliban spokesman, told Al Jazeera the group had not received any cash and claimed the reports were part of a campaign to discredit the Taliban.
An official in South Korea's presidential office also said on Saturday:"We deny any payment for the release of South Korean hostages."
"The two conditions for the release are that we pull out our troops and stop Korean missionary work in Afghanistan by the end of the year," said the official, who declined to be named.
Alan Fisher, Al Jazeera's correspondent in Kabul, said: "It is in the interests of both the Afghan government and the Taliban to deny reports of a ransom.
"But Al Jazeera has been told by more than one source on more than one occasion, one of them a senior figure in the Taliban, that a ransom, said to be around $20m, has been paid."
Meanwhile, the 19 Korean former hostages held for over six weeks by the Taliban are set to begin the final leg of their journey home.
The South Korean Christians are due to fly to Seoul on Saturday after leaving Afghanistan on a UN plane bound for Dubai the day before.
Song Min-Soon, the South Korean foreign minister, said the country had no choice about negotiating with the Afghan group while the lives of the 19 remaining hostages were at stake.
"We have to wish you to remember that innocent people were kidnapped and two of them were killed," he said.
"The government struggled to strike a balance between the international norms and custom concerning this kind of issue and the absolute premise that we have to save the people's lives," he said.
Rangeen Dadfar Spanta, the Afghan foreign minister, had earlier criticised Seoul for negotiating with the Taliban, saying it set a dangerous precedent that could lead to more kidnappings.
The group were part of a group of 23 missionaries kidnapped in southeast Afghanistan in mid-July.
The Taliban killed two male hostages and released two women as a 'goodwill gesture.'
Some of the 19 released hostages have told Al Jazeera in a series of exclusive interviews how they lived in constant fear for their lives during their captivity.
They said they were split up into small groups and moved around the Afghan countryside to avoid detection.
One Taliban member would tend to a farm by day and then grab a rifle and stand guard over hostages at night, they said.
Television footage of the freed hostages broadcast on Friday raised concerns about their health and the possible effect media exposure could have on their fragile emotional state, said Cha Seong-min, who has represented family members since the crisis began.
Seoul pull out
"I'm very much concerned because she looked like she lost a lot of weight," Cha said of his sister, Hye-jin, one of the 23 South Koreans captured.
The kidnapping was the largest in the resurgent Taliban campaign against foreign forces since US-led troops removed the Islamists from power in 2001.
The Taliban decided to free the hostages after Seoul restated its plan to pull all its forces out of the central Asian country.
Seoul had already decided before the crisis to pull its 200 engineers and medical staff out of Afghanistan by the end of this year.
It has also banned nationals from travelling there.