The 24-year-old France international is the subject of significant interest from Tottenham, where former manager at St Mary’s Mauricio Pochettino is now in charge.
Sky sources understand Schneiderlin is keen on a move to White Hart Lane and he made an explosive outburst on Twitter last week, stating his time at the Saints had been “destroyed in one hour” of a meeting with club officials.
Schneiderlin has been told to stay away from Southampton because his head is not right and he is not in the squad for their final friendly at home to Bayer Leverkusen on Saturday.
Boss Koeman said: "The situation is difficult because the player makes it difficult. I spoke to him with our chairman and the situation has not changed – we won't sell Schneiderlin and he has to accept that.
"I'm not so much angry because there's some different influences around the player. Maybe Tottenham is pressing the player, maybe the agent.
"Tomorrow he is not in the squad. He said he is not physically and, even more importantly, mentally prepared for the game. On one side I can understand that.
"We told him to take the weekend off and think about the situation but if this is still the situation next week then Morgan has a big problem.
“First of all, you have to know you signed a contract and you have to respect your contract. He will continue as a football player of Southampton. Now it is up to him."
Southampton were handed a boost on Friday, with club captain Jose Fonte signing a new three-year contract on the south coast.
And the 30 year-old defender hopes Schneiderlin will change his mind and stay this season.
“It is very simple. Schneiderlin is one of the best midfielders in the Premier League," said Fonte. “As a teammate I always want him in front of me – he has more interceptions and more tackles than anyone else and he runs miles.
“As the manager says, it is a difficult situation but, for us, we want him in the team and we will do everything we can to make him happy so he stays.”
Manager Koeman is still still looking to bolster his squad ahead of their season opener away to Liverpool, which is live on Sky Sports 1HD on Sunday August 17.
Saints are understood to be chasing Argentina and Sporting Lisbon full-back Marcos Rojo, while a deal is thought to be close for Steaua Bucharest defender Florin Gardos.
Koeman confirmed: "These two players are both on our list. We are interested in Gardos but until now they haven't told me it is signed or done.
"We are interested in Rojo but the transfer is a question for the chairman and (executive director) Les Reed."
You can watch Liverpool v Southampton live on our first Super Sunday of the season from 1.30pm on Sunday August 17.