Officials decided at a city council session on Tuesday to analyse what would be needed for a bid.
A member of the Bosnian Olympic Committee said separately that it would take less investment than the previous time, when some 80 percent of the facilities - including hotels, roads and telecommunications - had to be built from scratch.
"We need investment of about 20 to 30 percent compared with 1984," Ahmed Karabegovic, vice-president of the country's Olympic Committee and a leading organiser of the 1984 Games, told reporters.
"We are all aware of the destruction the war has brought... (but) preparations for and the staging of a Winter Olympic Games would boost sports and cultural life and also business activities in all areas," he said.
Most facilities in the city and on three of the four mountains used at the 1984 Games were damaged or destroyed during the 1992-1995 war.
Some, such as the Zetra sports centre in the city, were fully repaired after the conflict but Bosnia remains heavily reliant on international aid to keep its war-damaged economy going.
The one 1984 mountain venue not affected was the Bosnian Serb-controlled Jahorina, where the women's Alpine skiing events took place.
The Bosnian Olympic committee is expected to back the authorities' initiative this month. If Sarajevo decides to go ahead it will submit a bid at a later stage to the IOC, which will choose the hosts for the 2010 Winter Games in 2003.
Reuters
Sarajevo, which staged the 1984 Winter Olympics and was besieged a decade later during the Bosnian war, is considering another bid to secure the Winter Games in 2010.
