Sources close the negotiators said a mediation team made up of tribal chiefs and government representatives left the eastern region of Shabwa, where the family was seized, for Aden in the south to discuss the kidnappers' demands with local officials.
"The kidnappers are demanding a promise for the release of five of their colleagues or a commitment to arrest the real culprits of the local vendetta" held in Aden for which the five have been detained, one of the sources said.
The family of former German diplomat Juergen Chrobog was reportedly abducted about five days ago from a restaurant on the road between the port city of Aden and Shabwa, about 480 kilometres east of the capital Sanaa.
Tribal chief Sheikh al-Ahmar Ali al-Aswad is believed to be holding the Germans as bargaining chips for the release of five brothers he says were wrongly imprisoned by Yemeni authorities, a tribal source said.
It was the fourth abduction of foreign tourists in Yemen this year. Two Austrians were freed last week after being held for three days.
Nearly all the kidnappings have been carried out by tribesmen seeking to pressure the central government and hostages have generally been released unharmed.
In Berlin, a foreign ministry spokesman said Germany was trying to find a settlement by Saturday after Foreign Minister Frank-Walter Steinmeier called his Yemeni counterpart for help to settle the crisis peacefully.
"The life and physical integrity of the hostages has absolute priority," his spokesman Martin Jaeger said. "We hope that by tomorrow (Saturday) a solution will have been found."
Mr Jaeger said that Mr Chrobog, who ironically once helped free hostages held in Mali, had respected German security advisories for Yemen.
A Yemeni interior ministry official said on Thursday that the mediators "were equipped with guarantees to the kidnappers that their request would be examined and that a solution would be reached".
But a local newspaper quoted a kidnapper as warning that the tribesmen would move the German captives if security forces advanced towards their hideout.
"We will be sorry to force the German family to walk on feet for a long distance if we were forced to move," Ahmed al-Lahji told the English-language Yemen Observer, as security forces have reportedly encircled the hideout.
He insisted that the hostages were "guests" who are being treated well.
Despite its proximity to oil-rich Saudi Arabia, Yemen is one of the world's poorest countries and more than 200 foreigners have been kidnapped in the past decade.
While most cases have been resolved peacefully, three Britons and an Australian seized by Islamist militants were killed when security forces stormed their hideout in December 1998.