Zaliukas came on in the second half of the Ibrox club's pre-season friendly with Brora Rangers at Dudgeon Park in Sutherland yesterday.
And the former Hearts captain, a free agent after parting company with Sky Bet Championship club Leeds United, did well in his 45 minutes on the field.
The SPFL League One champions did not concede while Zaliukas was on the park and earned a 1-1 draw thanks to a late goal from comeback star Kris Boyd.
McCoist, who is also tracking former Scotland midfielder Don Cowie, will meet with Rangers chief executive Graham Wallace in the coming days.
And he will offer Lithuanian internationalist Zaliukas, who turned down the chance to sign a deal with the Light Blues after a trial last season, a contract.
McCoist has brought in Boyd, Darren McGregor and Kenny Miller during the close season as he prepares for the step up to the Championship next season. And he feels Zaliukas has the ability and experience to help Rangers beat Hearts and Hibs to the second-tier title and complete the final stage of "The Journey".
Rangers assistant Kenny McDowall has been pleased with the contribution Zaliukas has made on the Glasgow club's tour of the Highlands.
He said: "Marius's fitness is good. He was right up for it yesterday and was keen to play and be involved. We have obviously been delighted to have him."
Rangers needed Boyd, who made his first appearance for them in four years, to come off the bench and score to spare their blushes in Brora.
The Highland League champions dominated the first half and deservedly took the lead through an opportunistic James McKay strike in the 14th minute.
But McCoist, as he had done in the 3-0 win over Buckie Thistle last Thursday night, used 21 players in the pre-season match.
Only keeper Cammy Bell played the full 90 minutes. He once again gave kids like Robbie Crawford, Calum Gallagher, Luca Gasparotto, Craig Halkett, Barrie McKay and Andy Murdoch a chance to show what they are capable of.
McDowall was pleased with the Rangers performance in the second half and predicted the Murray Park youngsters would benefit from the experience they have gained.
He said: "It was a tough workout against a team that did not hold back. That is why we take these games during pre-season. We know that our boys are going to have to put a shift in to get a result.
"We started with some of the younger players in the first half once again. They need to realise how hard they need to work in games in order to get a result.
"If you go a goal behind then it can be a difficult to overturn that in a match and that is how it proved yesterday. But they showed a bit of class in the second half.
"The boys stepped up their efforts in the second period and on another day I think that we would have scored a few goals and got the result we were looking for."