Wali-ur Rehman, deputy head of the Tehreek-i-Taliban Pakistan (TTP), did not provide proof that the group had the pair but said they were in good health and demanded they be exchanged for a Pakistani scientist jailed in the US.
Olivier David Och, 31, and Daniela Widmer, 28, were abducted on July 1 while driving in Baluchistan, a sparsely-populated southwestern province bordering Iran and Afghanistan that attracts few tourists due to separatist violence and Taliban activity.
"The Swiss couple are with the TTP. They are at a very safe place," Wali-ur Rehman, deputy chief of the Tehreek-i-Taliban Pakistan (TTP) told news agency AFP by telephone.
"They are completely in good health, they are getting reasonable food and they have not fallen ill since they landed in our custody."
Rehman said the Taliban would release the couple if the US freed Aafia Siddiqui, a female neuro-scientist sentenced in 2010 for the attempted murder of US government agents in Afghanistan.
"We call upon the Western world to put pressure on America for the release of Aafia Siddiqui," he said. "If America does not agree to her release then our shura (council) will take a decision about the Swiss hostages."
Other Taliban sources confirmed TTP's claim and added that the hostages were now being held in the lawless border district of South Waziristan, a notorious haven for Taliban and al-Qaida bases.
The Swiss Foreign Ministry told AFP it had "taken note" of the media reports but said it would not comment on the information. It reiterated that authorities are "continuing with their efforts to bring the two Swiss citizens back safely to Switzerland."
Previous kidnappings in Pakistan have also been followed by a demand for Siddiqui's release, without effect. Rehman said the group had not issued a ransom demand.
Siddiqui, dubbed "Lady Qaida" by US tabloids, was jailed for 86 years in 2010 after being found guilty of grabbing a rifle at an Afghan police station where she was being interrogated and opening fire on servicemen and FBI agents. She missed and in a struggle was herself shot by one of the US soldiers.
The jailing of Siddiqui, a highly-trained scientist who was missing for five years before the shooting, sparked mass protests in Pakistan and the government vowed to fight to free her.
The Swiss couple's blue Volkswagen van was found abandoned after they were snatched in Loralai district, around 170 kilometres (100 miles) east of the Baluchistan capital Quetta. According to visas stamped in their passports, they arrived in Pakistan from India on June 28.
The pair entered Baluchistan from Punjab province and may have been heading for Quetta, possibly en route to Iran, officials in Islamabad have said.
Since 2008, Switzerland has advised against non-essential travel to Pakistan, citing risks including the threat of kidnapping. There was no immediate Swiss government comment Friday on the TTP claim.