The France midfielder has been targeted by north London rivals Tottenham and Arsenal, with his manager claiming he is "not mentally ready" to play for the St Mary's outfit
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But the St Mary's outfit have repeatedly ruled out a move, with chairman Ralph Krueger claiming the player would not become part of the exodus of players to have left the south coast outfit this summer.
And though Schneiderlin has claimed that not being allowed to leave has soured his six-year stay with the club, Koeman has backed up his chairman's claims, though the player is not "mentally ready" to play for the Saints.
"The situation is difficult, because the player makes it difficult and I spoke to Morgan with our chairman and the situation has not changed. We don't sell Schneiderlin and he has to accept that," he told Sky Sports News.
"He's not in the squad tomorrow [to play Bayer Leverkusen] because he said he's not in a physical, but even more not in a mental way prepared for tomorrow. On one side I can understand that.
"We said 'OK, we'll give you the weekend off to think about this situation'. And Monday morning we have [a] training session and we have one week [to] prepare for the first away match against Liverpool.
"He will continue as a football player of Southampton and now it is up to him."
Goal understands that Tottenham, and new manager Maurico Pochettino, are willing to wait until the end of the transfer window to sign a player who excelled under the Argentine's tutelage during his time in Hampshire.
But Koeman insisted that Schneiderlin will remain a key part of his plans moving into the new season as they prepare for their opening Premier League fixture against Liverpool on August 17.
"Of course [I expect him to stay]," he said. "I like that he will stay because he is also a very good player - a key player in the team - and we like to keep them.
"We lost some players and I think the club did a great job to bring in new ones but now we have to prepare for next week."