The new Saints boss has confirmed the club has put is foot down and is not willing to let the French international leave, despite the player handing in a transfer request
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 Saints boss Mauricio Pochettino.
The France international was a notable absentee from Southampton's 3-1 pre-season win over Brighton on Thursday.
But Koeman has no intention of parting ways with Schneiderlin, having already lost captain Adam Lallana, Luke Shaw, Dejan Lovren, Calum Chambers and Rickie Lambert ahead of the 2014-15 campaign.
"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.
And the Dutchman expects to add to his arrivals in the coming days, with Celtic goalkeeper Fraser Forster, Manchester United striker Javier Hernandez and Inter winger Ezequiel Schelotto all linkedto St Mary's.
"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.