The evacuation will be organised by the Red Cross and female police officers, Homs governor Talal al-Barazi told Syrian state news agency Sana.
The city is at the centre of direct talks currently taking place in Geneva, Switzerland between the Syrian government and opposition, mediated by the UN and Arab League envoy Lakhdar Brahimi.
Forces loyal to Syria's authoritarian president Bashar al-Assad have been laying siege to Homs or the past 18 months, destroying much of the city and blocking food supplies from reaching rebel-held districts.
Brahimi admitted on Monday the Geneva negotiations "haven't produced much".
He also said there was no breakthrough in attempts to arrange aid deliveries to besieged parts of Homs, Syria's third city.
The government has instead offered to allow women and children to leave opposition-held areas, and to grant safe passage to men as well if they receive a list of their names.
But the opposition has dismissed it as a ruse to displace and arrest its supporters.
Syria's third largest city, Homs has been a key battleground in the almost three-year-long uprising against Assad.
It was dubbed "the capital of the revolution" after residents embraced the call to overthrow Assad in early 2011 and much of the city fell under the control of the opposition.