Zaliukas has previously worn the captain's armband for Hearts
Manager Jim Jefferies is considering his options for the Hearts captaincy following Michael Stewart's departure.
Marius Zaliukas is a candidate, having assumed the skipper's role in Stewart's absence last season.
Jefferies told Hearts.TV: "Marius is out of contract at the end of December so that might have a bearing on it.
"There are a couple of other players who have caught our eye. We'll look at in terms of attitude and who we think might have a chance."
Meanwhile, Hearts owner Vladimir Romanov has launched a bid to take full control of the club's main sponsor, Ukio Bankas.
Romanov is a majority shareholder in the Lithuanian-based bank and, if his bid is accepted by the governing authorities in the Baltic state, he would obtain 100 percent ownership.
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