EU officials said Yanukovich himself would be excluded from such measures in order to keep channels of dialogue open.
As well as asset freezes and visa bans, ministers will discuss measures to stop riot gear and other equipment being exported to Ukraine and could consider arms restrictions.
Diplomats said the threat of sanctions could also target assets held in the West by Ukrainian business oligarchs who have either backed Yanukovich or are sitting on the fence.
The United States, going head to head with Russia in a dispute reminiscent of the Cold War, urged Yanukovich to pull back riot police, call a truce and talk to the opposition.
Obama warned the Ukrainian armed forces that the crackdown could damage "our defence relationship". But Washington appears to have little direct leverage in Kiev.
Russian President Vladimir Putin, who has met Yanukovich six times since the crisis began, has kept quiet on the flare-up. But Foreign Minister Sergei Lavrov blamed the West for encouraging opposition radicals "to act outside of the law."
Moscow said on Monday it would resume stalled aid to Kiev, pledging $2 billion just hours before the crackdown began. The money has not yet arrived, and a Ukrainian government source said it had been delayed until Friday "for technical reasons."
Putin's spokesman said on Thursday that Moscow was waiting for the situation to normalise before paying up. Ukraine's hryvnia currency, flirting with its lowest levels since the global financial crisis five years ago, weakened again on Thursday.
Possibly due to the risk of sanctions, three of Ukraine's richest entrepreneurs have stepped up pressure on Yanukovich to hold back from using force.
"There are no circumstances which justify the use of force toward the peaceful population," steel and coal magnate Rinat Akhmetov said in a statement late on Tuesday.
Akhmetov, who partly bankrolled Yanukovich's election campaign in 2010 and whose wealth is put by Forbes at more than $15 billion, said: "People's deaths and injuries on the side of protesters and the security forces in street battles are an unacceptable price for political mistakes."
Viktor Pinchuk, another steel billionaire known in the West for his philanthropic activity, said: "A peaceful solution must be found. It is imperative to refrain from the use of force and find a compromise."
Dmytro Firtash, a gas and chemicals magnate who is part owner of a popular TV channel, said in a statement: We, through our joint actions, must end the bloodshed. We are against radical actions by whomever it might be."