The 23-year-old Belarus international striker has been given a two-week trial by the Tynecastle club with a view to a January transfer from his current club MTZ-RIPO Minsk.
Belarus striker on trial
"Vyacheslav will arrive at Hearts next week for training. The Belarussian season is over so he can do this," Hleb's agent Nikolai Spilevski told the Scottish Sun.
"They will take two weeks to decide whether or not he will stay there but there is a chance this could become a permanent deal."