The Daily Record claims that Stoke City and West Bromwich Albion were also interested in the 24-year-old defender.
According to BBC Sport, Celtic are set to sign the Denmark international for a transfer fee of £1.5 million. It was reported on Saturday afternoon that the defender was having a medical with the Scottish Premiership giants.
Sviatchenko has been at Midtjylland his entire professional career so far and has Champions League experience with the Danish side.
Celtic are at the top of the Scottish Premiership table at the moment with 49 points from 21 matches. The Glasgow giants are six points clear of second-placed Aberdeen and are on course to win the league title yet again.