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 €25 million move to Liverpool, with Romanian defender Florian Gardos widely reported to be close to a switch to St Mary's Stadium.