The Dutchman's contract is up at the end of the 2016-17 season and his work at the club has reportedly been viewed well by the directors.
Koeman arrived in 2014 after the departure of Mauricio Pochettino and key players such as Luke Shaw, Rickie Lambert, Dejan Lovren and Adam Lallana, before then losing the likes of Morgan Schneiderlin and Nathaniel Clyne before the start of this season.
Still, the former Barcelona star managed a seventh-place finish in 2014-15, one better than the eighth-place finish Pochettino achieved the season prior, and could still better that again this season.
Southampton sit seventh with two games to play and trail fifth-placed West Ham by just two points.
"I had a short talk with [head of football development] Les Reed about the future and I said, 'Let's have a coffee and a talk after the last game'," he said.
"Everybody knows I have left one year's contract but if the club likes to have a talk about that I will listen.
"First we have to talk and then conclude something. It’s nice to be wanted by Southampton because that is the club where I worked also for one more year."
Koeman suggested a key part in his decision making process would be whether or not the club would be able to keep its best players.
"If it is realistic I don’t know but of course you want to keep everybody; keep the best players and still have a stronger team next season than we have this season," he said.
"We will see what Les tells me. It is not about today."