Quoting an unidentified diplomat, German television station N-TV on Friday reported that the group has demanded $5.2 million for releasing each hostage.
The television station said talks between the authorities and the hostage takers for securing the release of the hostages were in a very active phase.
Reporting from Mali, the station’s reporter also said the tourists were safe.
“They are in a satisfactory condition but they are tired,” he said, adding that “letters from the hostages had been handed over by an intermediary.”
The 14 tourists, including nine Germans, four Swiss and one Dutchman, are believed to have been abducted by the Salafist Group for Preaching and Combat (GSPC).
They went missing in batches some four months ago while traveling in Algeria’s vast Sahara desert without local guides.
GSPC is suspected to be a radical Islamic group and Algerian authorities say it has links to al-Qaeda.
Seventeen other tourists abducted in the same area were freed in a raid by Algerian special forces in May.
But rescuing the others is proving difficult.
“The desert is huge, it is not easy to find someone there,” an Algerian official said.