The 23-year-old Dane, who has made close to 100 appearances for the Superligaen outfit, was made vice-captain of Midtjylland at the start of the 2013/14 season.
The 6ft 1in centre half has made two appearances for his country, making his debut in Denmark’s 3-2 friendly win over the USA.
However, Celtic will likely face competition from LOSC Lille, Stoke and English Premier League newcomers AFC Bournemouth.
German side Augsburg had been linked with the defender but are believed to have scaled back their interest.
Sviatchenjko is a team-mate of former Celtic striker Morton Rasmussen and ex-Hibs defender Francis Dickoh.