The left-back moved to St Mary's from Chelsea on a temporary deal in the summer, and Koeman has claimed that if the club allow it, Bertrand could become a permanent Saints player.
"If we have the money, yes," the Daily Echo quotes Koeman as saying. "If it's up to me, yes. Maybe it's too early to talk about that, but I am very happy until now with the performance of Ryan."
Southampton, whom many had tipped for relegation this season, are currently third in the Premier League table after winning five of their eight fixtures.