"We have confirmed information that they are still alive. They are five Germans and a British national," deputy prime minister for defence and security affairs, Rashad al-Aleemi, told a press conference.
"The three possible places they could be in are Maarib, Al-Jouf and Saada," he said.
The family from Saxony has not been seen since they were abducted along with four other foreigners in the country's Saada province in mid-June. Authorities there believe that the kidnappers may be Shiite rebels from the mountainous region near the Saudi border.
Three of the hostages – two German women and a South Korean woman - were found murdered by Yemeni authorities three days later.
Foreigners are often kidnapped in Yemen by tribesmen to be used as bargaining chips in disputes with the government. More than 200 foreigners have been abducted over the past 15 years.