'Sky Sports' have reported that intitial talks are taking place between the clubs.
Vestergaard was part of Denmark's World Cup team in Russia, and also caught the eye of West Ham bosses.
The 25-year-old was an unused substitute in all four of Denmark's matches.
Vestergaard made 32 appearances in the Bundesliga last season, and scored three goals.
He has been playing in Germany since 2011, where he had spells with Hoffenheim and Weder Bremen.
Southampton's boss Mark Hughes has already made two signings this summer, bringing in winger Mohamed Elyounoussi and Stuart Armstrong, from Basel and Celtic respectively.