Officials said Juergen Chrobog and his family, who were seized by Yemeni tribesmen on Wednesday during a trip to Shabwa from the southern port city of Aden, are in good health.
German media, quoting Yemeni a government official, said the hostages were expected to be released on Friday night. Germany's Foreign Mministry declined to confirm the report.
"Progress is being achieved in a positive way and talks are being led by the defence minister (Abdullah Ali Aleiwa) himself who is from the same province (as the kidnappers)," a Yemeni official told Reuters.
"We are increasing pressure on the kidnappers to gain the safe release of the Germans," he said, adding that he had information that the hostages were in good health and being treated well.
The kidnappers are demanding that the Yemeni government free five tribesmen jailed on criminal charges including murder.
Residents said government forces have surrounded the area where the tribesmen live. But Yemeni officials have said no force will be used to free the hostages, who they say were seized by members of the al-Abdullah tribe.
Frank-Walter Steinmeier, the German foreign minister, said on Thursday he was in regular contact with Yemeni authorities, and expressed hope the German diplomat and his family would be freed soon.
"Talks are being led by the defence minister (Abdullah Ali Aleiwa) who ishimself from the same province (as the kidnappers)"
Armed tribal groups in Yemen, where central government control is often weak, seize tourists frequently, but they are usually freed unharmed after negotiations.
Chrobog, 65, was Germany's ambassador to the US from 1995 to 2001. In 2003, he was the top diplomat dealing with Europeans abducted in the Sahara desert and was able to secure the release of 14 hostages, including nine Germans.