Schneiderlin handed in a transfer request during the week after criticising the club on Twitter for blocking a move to Premier League rivals Tottenham, managed by former boss Mauricio Pochettino.
The France international was a notable absentee from Southampton's 3-1 pre-season win over Brighton on Thursday.
"It's the decision of the board but I don't talk about it," Koeman told Sky Sports News. "He's a player at Southampton and he will continue as a player at Southampton.
"But I don't like to talk about that situation. I spoke to Morgan two days ago and he is still not in the shape to play a friendly at this level. He needs more training sessions. If he's ready he will play.
"Normally he will play next week against Bayer Leverkusen [Southampton's final pre-season friendly]."
While the core of Southampton's squad has been pulled apart, Koeman has attempted to fill the void by signing Dusan Tadic and Graziano Pelle, and Ryan Bertrand on a season-long loan deal.
"There is no news on that and still no news on other players," he said. "We are close to signing two or three players and we hope to do that by this weekend.
"I won't talk about any of the players but we are looking to bring in players into this squad at the level that we need to have a good season."
Southampton's first Premier League fixture of the season is against Liverpool at Anfield on August 17.
