They are unable to get any help from Bangladesh, as it does not have any mission there.
Foreign ministry officials in Dhaka said on Sunday that they were trying to rescue the two Bangladesh nationals through the country’s embassy in Kuwait.
The two men have been identified as Golam Mostafa and Sirajul Haque.
Houthi rebels in Yemen have recently seized the capital city.
Golam Mostafa told bdnews24.com over phone that he had found the situation in Sana deteriorating when he arrived in Yemen a month ago.
He said there were no flights due to airstrikes every day.
Mostafa said he had contacted the missions of India and Pakistan there but both had expressed their inability to help a foreigner.
“Saudi Arabia, Kuwait, Qatar withdrew their embassies a long time ago. Now, I don’t know what to do,” Mostafa said.
He said he was staying at Shahran Hotel and the other Bangladeshi engineer, Sirajul, in an adjacent hotel.
The UN, too, has evacuated close to 100 of its international staff from Sana’a, which has been under Houthi control since September.
Airport officials said up to 250 other foreigners working for international oil companies and NGOs had also flown out to Ethiopia and Djibouti.
Pakistan, which is yet to decide whether to offer military support to the Saudis, is flying jumbo jets to Yemen to evacuate hundreds of its nationals, a Defence Ministry official said in Islamabad on Sunday, after TV pictures showed distraught families pleading for help.