The defender joined the Scottish Premiership leaders earlier in the window for £1.5m.
The 24-year-old joined Ronny Deila's men earlier in the month from Danish side FC Midtjylland for around £1.5m (via BBC Sport), and while the defender has yet to appear in a competitive fixture for the Hoops, McGregor hinted that he has seen enough to suggest that the Dane will improve the squad.
"We've got Sviatchenko to come in as well and the boys are looking forward to seeing what he brings to the team," he said, as reported by The Scottish Sun.
"He's a suave big guy and he fancies himself a wee bit. But he's a nice big lad so he should fit in pretty well with the boys."
Sviatchenko has arguably got a difficult task on his hands if he is hoping to cement a starting spot in Deila's side in the very near future. Efe Ambrose and Jozo Simunovic have formed an excellent partnership in recent weeks, and the manager may have doubts about tampering with a winning formula.
The pair have started the last five games together, and in that time, the club have recorded five wins with two clean sheets.
And with his side having only conceded 19 league goals all campaign, Deila is likely to find it difficult to find a reason to drop either of the pair to allow for Sviatchenko to come into the side.