Zaliukas, 26, reported an improvement in his condition both on Sunday and Monday and looks set to keep his place for the trip to Ibrox on Saturday.
Jose Goncalves could also be in line to face Walter Smith's side, with the defender due back in training this week following a successful course of treatment on his injured thigh in Germany.
Manager Csaba Laszlo told his club's official website: "I don't know exactly what the situation is with everyone as I'm not back at the academy until Tuesday.
"It is the players' day off (Monday) but definitely I want as many of our important players fit and back in the team.
"If we can get them all back then this is positive news."
Rangers 1/3, Draw 4/1, Hearts 8/1
Source: Team Talk
Source: Team Talk