The northern city of Harbin, which hosted the Winter University Games earlier this year, submitted a bid proposal to China's State Council last month, while 2007 Asian Winter Games venue Changchun in Jilin Province was also reported to be interested.
China must inform the International Olympic Committee (IOC) of the name of any bid city by October 15.
Liu said: "Harbin and Jilin both have had experience in hosting international winter competitions.
"Whether to bid for Winter Olympics firstly depends on the enthusiasm of the potential host cities.
"If they are really enthusiastic to bid we will certainly support them."
Liu, who is a member of the State Council, said last month that a Chinese bid to host a Winter Games in 2018 would be "difficult".
Heilongjiang Province spent 3.1 billion yuan (£276.6 million) on building Olympic standard facilities for this year's Winter University Games in Harbin, including the venue for China's first accredited Alpine skiing downhill race.
Governor Li Zhanshu said Harbin would not give up if they failed to win, as they did in their bid for the 2010 Games.
He said: "If we fail again in the bid for the 2018 Winter Games, then we are determined to win the 2022 Games.
"To host the first ever Winter Games in China is our dream."
Potential candidates already declared for 2018 include Annecy in France, Pyeongchang in South Korea and Munich, which is bidding to be the first city to host both the Summer and Winter Olympics.
Denver are also expected to enter the race if Chicago fails to win the vote to host the 2016 Olympics, a decision due to be taken by the IOC at its Session in Copenhagen on October 2.
The winning city will be chosen on July 6, 2011, at the IOC Session in Durban.
August 2009: Harbin still hopeful on 2018 Winter Olympic bid
May 2008: China considering bid for 2018 Winter Olympics