The Aston Villa defender won many admirers for his performances at the World Cup for Netherlands and the new Saints boss sees him as "a perfect addition to every group"
The Netherlands international excelled as Louis van Gaal’s side finished third at the World Cup over the summer, sparking speculation of a move elsewhere.
Koeman has previously indicated his interest in the centre-back but has now gone further, declaring Vlaar “a perfect addition to every group”.
"Vlaar became one of the best Oranje defenders at us, at Feyenoord [my old club]," he told Helden,. "And, at the last World Cup, he became one of the best of the tournament.
"He's a perfect addition to every group and a real leader. I would really like to have him at Southampton."
Koeman is in the market for a centre-back after Dejan Lovren's £20 million move to Liverpool, with Romanian defender Florian Gardos widely reported to be close to a switch to St Mary's Stadium.