The 29-year-old defender has been a free agent since leaving Tynecastle during the summer.
Leeds have taken the player on trial after he failed to secure a permanent deal with fellow Championship side Queens Park Rangers.
"He came on the radar a long time ago. He's been at QPR and he's an experienced player. He's here for a number of days and he has a good pedigree," McDermott told Leeds United's official website.
"He's 29, he's captained Hearts, and to have that bit more experience is important. We have some good young centre-halves here, but to add to that with some experience would be good."
Zaliukas has won 20 caps for Lithuania.