Zaliukas helped Hearts keep a clean-sheet against Aberdeen
Hearts manager Jim Jefferies hopes Marius Zaliukas will agree a contract with the Edinburgh club next week.
The captain has been frozen out of the team as talks stalled but returned to lead Hearts to a 1-0 win at Aberdeen.
"There has been a lot of progress and we're almost there but nothing has been signed and sealed yet," said Jefferies.
"Hopefully, things will get tied up and there's no last-minute snags. We were just delighted that he was playing. You saw the difference he made."
Zaliukas, who has been on loan from Kaunas since 2006, was playing for the first time since August and Hearts turned in a mean defensive performance at Pittodrie, while always looking a threat on the break.
Kevin Kyle headed home the only goal of the game, nodding past groggy goalkeeper Mark Howard early in the second half.
Howard, who had earlier made good saves to deny Calum Elliot and Suso Santana, was hurt in an awkward fall before the interval and was replaced as soon as the visitors scored.
"The balance of the side is right," added Jefferies, reflecting on the victory.
"I thought we looked solid at the back, it was a right good away team performance.
"There was a determination about the players and I think they got a wee lift from Marius being back.
"If anything, I thought we maybe deserved to win it by another goal or two."
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