The Lithuanian centre-half has been without a club since leaving Tynecastle over the summer at the end of his contract.
A trial spell at Queens Park Rangers failed to see terms tabled, so Leeds have offered the 29-year-old another opportunity to prove his worth at Championship level.
McDermott told the club's official website: "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.
"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."
While Zaliukas would be available on a free if he does enough to catch the eye, McDermott revealed that he still has funds at his disposal for the right loan agreements.
He added: "I've made six enquiries for players we targeted. For whatever reason, we couldn't get them over the line.
"I know I've said it before, but I'm not going to take players for the sake of it. There is money to bring loan signings in if we can find the right one."
Meanwhile, it has also been revealed that Leeds are planning to open contract talks with promising midfielder Alex Mowatt - a product of their academy system who has not looked out of place since joining the senior ranks.
McDermott said in the Yorkshire Evening Post of an 18-year-old talent who has started the Whites' last three games: "You're constantly monitoring players' contracts.
"Alex has got a year-and-a-half to go here but he's done extremely well so we need to speak to him and his people.
"Everyone knows what I think of him and how well he's done. He's got real ability."