The 24-year-old is reportedly on the Saints' radar for the January transfer window.
Ronald Koeman may have got off to a flying start as Southampton manager but the Dutchman is far from content with resting on his laurels.
The Saints are second in the Premier League table after a sensational opening to the league campaign and have the best defensive record in the top flight.
It is in all departments that Koeman's side are flourishing, however: in goal, defence, midfield and up front.
But Southampton are said to be looking to strengthen their midfield nevertheless.
The 24-year-old Slovenian recently played against England but little more than that is known on these shores by the masses, except for the fact that he has previously been linked with the likes of Liverpool and Everton.
Southampton, though, reportedly feel he is good enough to bring to St Mary's. And they may have been helped by a recommendation from Sadio Mane.
The striker signed for Koeman's side from Salzburg this summer and played alongside Kampl during his time in Austria.