Tymoshenko, who is serving a seven-year sentence for abuse of office, insists she is innocent and accuses Yanukovych of ordering her imprisonment in order to bar her from challenging him in the 2015 presidential election.
Demyanuk, the prosecutor, was quoted by Interfax as saying prosecutors would likely ask the court to arrest Vlasenko, but Prosecutor General's spokeswoman Margarita Velkova told The Associated Press that prosecutors had already petitioned for him to be granted bail.
Parliament is scheduled to vote Wednesday on a bill that would permit Tymoshenko to travel to Germany for medical treatment, but Yanukovych's allies have opposed it. Two top EU envoys are set to deliver a crucial report on the case in Brussels on the same day.
Yanukovych may hope that the EU will drop its demand for Tymoshenko's release out of fear that Ukraine would opt for closer ties with Russia.
Over the weekend, Yanukovych made a surprise trip to Moscow for talks with Russian President Vladimir Putin. Recent comments made by Ukraine's Prime Minister Mykola Azarov on the importance of good economic ties with Russia also suggest that Kiev is considering a tilt toward Moscow.
Yatsenyuk warned that Parliament's reluctance to pass the bill and Vlasenko's questioning signaled Yanukovych's readiness to abandon the deal with the EU ahead of a summit in Vilnius, Lithuania.
"This means a failure of the Vilnius summit. This is the main task that has been put forward," Yatsenyuk said on his party's web site.