Vestergaard has been released by Southampton to travel to Leicester to undergo a medical and discuss personal terms.
"He [Vestergaard] is doing the medical check and when that is done, then the deal is done, said Southampton head coach Ralph Hasenhuttl.
"He will go to Leicester, then it is for us to replace him and this is what we will do in the future."
Vestergaard has been on the wishlists of Leicester City for quite a long time after they tried to sign him in January 2020.
Following the injury of Fofana the Foxes have been assessing their options to sign Vestergaard.
Fofana, has been ruled out until 2022 with a medial ligament injury and the arrival of Vestergaard seems to be a replacement for the French defender.
Fofana got injured after a harsh tackle from Fer Nino and had to leave the pitch on a stretcher in Leicester's pre-season friendly against Villarreal at the King Power Stadium last week.
Vestergaard played in all six of Denmark's games at the Euro 2020 as they reached the semi-finals.
The bulky centre-back joined Southampton on a four-year contract in 2018 from German Bundesliga side Borussia Monchengladbach.
Featuring thirty times with 3 goals for Southampton last season in the Premier League, Vestergaard helped the Saints finished 15th in the league log.
Leicester City boss, Brendan Rodgers speaks on the need of signing the Danish defender.
"Without going into detail before Jannik is confirmed as a signing, it was pretty clear we needed a centre-half," said Rodgers. "That's probably what sparked the interest. We were very light in the area.
"It's a great tribute to the club that we could get our work done very quickly and see if we could sign a player of quality. Once we have that done, I can speak more on it."
