However, the Rangers manager also revealed that Jon Daly, his top scorer last season, is set to undergo knee surgery and will be sidelined for up to six weeks.
Zaliukas is a free agent after being released by Leeds United at the end of last season. The 30-year-old centre-half joined Rangers on their pre-season tour of the Highlands last week and has impressed the Ibrox club's coaching staff in training.
McCoist, who added former St Mirren defender Darren McGregor last month to his squad last month, said the Lithuania international will be offered a contract in the coming days.
Zaliukas had the opportunity to join Rangers when he left Tynecastle, where he had played for seven years, last summer but opted to move to Leeds instead. However, he made just 13 league starts for the Elland Road club and his contract was terminated by mutual consent.
McCoist, who is poised to give the defender his Rangers debut in a friendly with Brora Rangers this afternoon, believes acquiring Zaliukas will increase his side's chances of beating Hearts and Hibs to the SPFL Championship next season and completing their return to the top flight.
"He looks fine in training and we certainly like the look of him as player," McCoist said. "I would imagine we'll sit down early in the week and try to get something done.
"We will sit down with the chief executive and see what we can do. I have certainly seen enough already that convinces me we need to try to sign him. We would be very keen to take it to the next step.
"We have good physicality about us already, but Marius can look after himself. We want to play good football, but we need boys who can handle themselves.
"The Championship will be a huge test for us all. It's going to be competitive and everyone knows what's at stake. I need to make sure we have a squad that can meet the challenge.
"Marius has played at the top level, he's played international football, and I think he has the experience we are looking for."
McCoist, who has also signed Kris Boyd and Kenny Miller this close season, remains keen to bring in former Cardiff City midfielder Don Cowie, but stressed that more players may need to leave Ibrox in order to free up the money needed to sign the Scotland cap.
"Don is a player we like and we are certainly interested in," McCoist said. "But it all depends on what kind of budget is left before we can look to take it further.
"I will need to sit down with [chief executive] Graham Wallace early next week because obviously other clubs will be interested. We might need to trim our own squad first; I'll just need to wait and see."
McCoist is relieved to have signed Boyd and Miller as Daly, who did not travel to Brora due to his injury, will miss the start of the season. He said: "Jon needs an op on his knee. The cartilage needs trimmed and he'll go in next week. I would presume it will keep him out for five or six weeks which is a bit of a blow.
"But it backs up what I have said all along. We need a big squad. We were looking to start the season with four strikers and that's us down to three. It's a blow to lose big Jon. Obviously Kenny and Kris will get a lot of attention, but he scored 25 goals last season.
"I was looking for him and Nicky Clark to kick on. We have signed two bigger names, but I don't want anyone to forget Nicky and Jon."
Boyd has had a clean-up operation on his ankle was left out of the team for the opening pre-season friendly with Buckie Thistle on Thursday night.
However, the former Scotland striker was put through a punishing training session at Brora's Dudgeon Park yesterday and McCoist is hopeful he will play 45 minutes.
He said: "We gave Kris a really good run-out, so we'll see how he reacts to it. We'll see how he is first thing. But I'd love to get him off and running."