The former Hearts defender impressed during a trial stint at Murray Park and has been offered a Gers contract following talks with chief executive Craig Mather last week.
Light Blues boss Ally McCoist said: "Marius trained very well with us and I know Craig had a chat with the board and myself then put an offer to him.
"He has now gone back home to contemplate it and to have a think, so hopefully, we will hear from him soon.
"We, as staff, feel we should strengthen in the centre of defence, although with that said, when you're getting hat-tricks from one of your centre-halves it's always encouraging and pleasing.
"I just feel, though, we need to think about the longer term and it's an area we definitely need to bring someone in."
After seeing off Arbroath 5-1 on Saturday, McCoist's side are in Ramsdens Cup action tonight when they face Queen of the South.
And McCoist has major injury doubts over two Gers stars ahead of the trip to Palmerston.
He said: "We've got one or two niggling injuries.
"We've got Lee Wallace still, Lewis McLeod looks very doubtful, and obviously Ian Black is out.
"And there's one or two of them carrying bumps and bruises.
"But the big doubts again would be Lee and certainly Lewis.
"Lewis got a whack on his knee. It's the same knee he's had trouble with, but not the same injury. So I think we'll need to protect him.
"He's got a fitness test tomorrow, but I'd have big doubts about him making it."