Vestergaard has reportedly popped up on Tottenham Hotspurs’ radar, with Jose Mourinho’s side ready to snap another top performer from the Saint Mary’s stadium for a second straight season. Pierre Emile-Hojbjerg joined Tottenham from Southampton before the start of the season.
But Hasenhuttl is keen to prevent lightning from striking twice and underlined his intentions of seeing Vestergaard remain on the South Coast.
Asked about the speculation regarding the Denmark international's future, Hasenhuttl replied: "What can I say? It’s nothing new when players who did a good job for us this season are on the list for some bigger clubs.
"This is normal. This has always been in our history.
"I don’t want to discuss rumours around there, it is not necessary to discuss it.
"You can be sure that this player has a contract for Southampton Football Club and as long as he has this, he’s our player and we will do everything to keep him here and to protect him for everything."
Vestergaard’s contract with Southampton expires in the summer of 2022.
The 28-year-old joined Southampton from Bundesliga side Borussia Monchengladbach in the summer of 2018 and has made 23 appearances in the Premier League this season, scoring three goals.