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 it would take less investment than the previous bid, when some 80% of the facilities and infra-structure had to be built from scratch.
"We need investment of about 20-30% compared with 1984," Ahmed Karabegovic, vice-president of Bosnia's Olympic Committee and a leading organiser of the 1984 Games, told reporters.
International support
"We are all aware of the destruction the war has brought (but) preparations for and the staging of a Winter Games would boost sports, cultural life and 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, were fully repaired after the conflict but Bosnia remains heavily reliant on international aid to keep its war-ravaged economy going.
The one 1984 mountain venue not affected was the Bosnian Serb-controlled Jahorina, where the women's 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.