Koeman likes Rojo's versatility, with the Argentina international comfortable at left-back and centre-half.
The Saints manager needs to find defensive cover after losing Luke Shaw to Manchester United, Calum Chambers to Arsenal and Dejan Lovren to Liverpool.
O Jogo says Southampton have opened talks with Sporting over a €15 million deal for Rojo.
Sporting are prepared to sell the World Cup veteran before the start of the season.