Zaliukas in talks over extending Hearts stay
The international defender has been on loan from FBK Kaunas - who are also owned by Hearts majority shareholder Vladimir Romanov - since summer 2006 but the agreement expires at the end of December.
Jefferies granted the 26-year-old permission to fly back to his homeland earlier this week as injury prevented him from participating in Tuesday's Co-Operative Insurance Cup victory over Elgin City.
Zaliukas' past disciplinary concerns didn't worry Jefferies when he handed the centre-half the armband at the start of the season and he is keeping his fingers crossed that an agreement between the player and club can be reached.
Speaking ahead of Sunday's SPL visit of Dundee United, Jefferies said: "He is actually not with us at the moment, he is in Lithuania. We had a day off on Wednesday and, with him being injured for the Elgin game, he set off and he is over there for talks.
"The situation is quite simple, he is a Kaunas player and I think he is out of contract with us very shortly. Maybe they're trying to sort something out just like Adrian Mrowiec. He is no longer with Kaunas, he is a Hearts player now and they're trying to do something similar with Marius so we've given him permission to go there.
"I made him captain, he is a good player and there is a really good spirit about the place in the dressing room right now that's totally different. It's buzzing, they're all enjoying it and he's part of that so I hope the talks go all right and he will be back here on Friday to prepare for the game on Sunday."
In two defeats and two draws to United - who were crowned the third force in Scottish football - Hearts failed to score a single goal against the Tannadice outfit last season. And Jefferies sees the weekend's match as a chance to signal their intent to wrestle that title away from their visitors, especially with United returning from a chaotic Europa League clash in Greece against AEK Athens.
Jefferies, who does not have his injury problems to seek with Zaliukas, Lee Wallace, Darren Barr and in-form striker Calum Elliot struggling, said: "I would love to go into the international break after winning the game.
"Then you could say that there is now a base to kick on and do what we set out to do, and that's to be at the right end of the table competing.
"This is probably a test the fact that everyone will be looking at Dundee United being away and this might be a chance."