Despite Saints wanting to hold out for £18m for the Danish defender, the South Coast club have reportedly accepted a £15m offer from the Foxes.
Vestergaard, who signed for Southampton from Bundesliga side Borussia Monchengladbach in July 2018, is said to have already agreed terms with Leicester and the deal will be confirmed once he completes a medical.
“He is doing the medical check, and, when that is done, then the deal is done,” said Hasenhuttl in his pre-match press conference ahead of Southampton’s visit to Everton on Saturday.
“He will go to Leicester, then it is for us to replace him and this is what we will do in the future.”
Southampton transfer news: Saints sign THIRD Chelsea prospect of the season
Saints transfer update: Southampton complete transfer for Adam Armstrong
Leicester boss Brendan Rodgers has been forced into signing a centre-back after prospect Wesley Fofana suffered a broken leg in a pre-season friendly against Villarreal last week.
The Foxes have been linked with signing Vestergaard since January 2020 and it looks like they finally have their man as the Dane had just one year remaining on his contract and Saints decided to cash in.
Vestergaard had his strongest season as a Saint in 2020-21, playing a leading role at the back in the early stages of that campaign before suffering injury.
The Denmark international then had a strong showing with his country in this summer’s EURO 2020 tournament, helping his side make it to the semi-finals.
With this reported £15m coming back into the club’s coffers, Hasenhuttl said Southampton will be signing a replacement.
“We’ve made the squad bigger, with players with a future at this club,” said Hasenhuttl. “There is still one position to fill because we have lost Jannik.”