Koeman has admitted he is unsure whether Schneiderlin or centre-back Toby Alderweireld will be at St Mary’s this season.
Midfielder Schneiderlin, who reported back for pre-season training today, and defender Alderweireld were stand-out performers in the last campaign as Saints finished seventh in the Barclays Premier League, their highest placing in the division.
However, France international Schneiderlin has been heavily linked with a move away, with Manchester United said to be ready to unveil a £24million deal for the 25-year-old.
But while Koeman revealed the Red Devils have not yet tabled an official bid for the player, the Dutchman is fearful of Schneiderlin being lured away.
“We have some doubts about players,” he said.
“We have the situation with Morgan Schneiderlin, we will have to wait what will happen.
“Until now, we have not had a serious bid for him from Man United. We will wait, but OK – that’s business that normally starts from now.”
Belgium centre-back Alderweireld, meanwhile, has returned to Spanish giants Atletico Madrid after his loan spell on the south coast reached its conclusion at the end of last season.
“The player likes to stay, we like to keep the player but it’s a little difficulty at the moment with Atletico Madrid, I have a good hope he will stay for Southampton,” added Koeman of the 26-year-old Alderweireld.
Southampton’s top-half finish was in spite of them selling a host of key players last summer, including Adam Lallana, Dejan Lovren, Rickie Lambert and Luke Shaw.
Koeman insists a similar clear out will not happen this time around, though
He added: “We have the experience from last season – it will be not the same this season, but we are prepared for everything.”