Schneiderlin held talks with Koeman and chairman Ralph Krueger on Friday morning where it was decided the midfielder was not "mentally prepared" to play on Saturday in a friendly against Bayer Leverkusen.
The 24-year-old has the weekend off and will be given until Monday to come to terms with Southampton's stance on his future.
"We made the decision about tomorrow's match together
If this is still the situation next week then Morgan has a big problem," Koeman said.
"It's not an easy situation
I was a football player and moved from smaller clubs to bigger clubs.
"But first of all, you have to know you signed a contract and you have to respect your contract.
"We told Morgan to take two days off and think about the situation - because we will not change our minds
This is our decision
So we will see on Monday."
Schneiderlin, who joined the Saints as an 18-year-old in 2008, has attracted interest from both Tottenham and Arsenal this summer.
He is understood to be keen on a move to White Hart Lane and a reunion with manager Mauricio Pochettino, with whom he enjoyed a close relationship at Southampton.
"I'm not so much angry because there's some different influences around the player," Koeman said.
"Maybe Tottenham is pressing the player, maybe the agent is pressing the player - it's a difficult situation.
"I understand that situation, I know from my experience how it works but we have to do what is the best for Southampton.
"That is my job and even if I, in some ways, understand his situation I have to do the best for the club and that is keeping these kind of players."
Schneiderlin experienced relegation to League One in his debut season at St Mary's before helping the club reach the Premier League with successive promotions.
He has been a leading figure among a talented group of Saints players, several of whom have been allowed to leave this summer with Rickie Lambert, Adam Lallana, Luke Shaw, Dejan Lovren and Calum Chambers all departing.
"No, it is not unfair (that he has not been allowed to leave like the others) - unfair is signing a new contract and wanting to go, that's unfair," Koeman said.
"Not every player is the same and not every situation is the same."
Koeman continued: "Even the situation when Dejan Lovren started pre-season, it was a little bit different.
"He had the same desire to move and finally the club accepted the bid.
"We can help the player and there is always a way back because I, as manager, will do what the best is for the club."
Saphir Taider became Koeman's fourth signing of the summer this week following the arrivals of Dusan Tadic, Graziano Pelle and Ryan Bertrand.
Taider arrives on loan from Inter Milan with troublesome striker Dani Osvaldo going the other way in exchange.
"Taider will bring quality," Koeman said.
"He's still a young player, he's still 22 and he will bring real competition between the midfield players and we need that."
The Saints boss confirmed the club are trying to complete deals for Sporting Lisbon's Marcos Rojo and Steaua Bucharest's Florin Gardos while adding he also wants another striker.
One player who will be at St Mary's this season is Portugese defender Jose Fonte.
The 30-year-old, who joined in January 2010, has signed a new three-year contract and will be the team's captain on the field this season
Kelvin Davis remains club captain.
"There was interest from other clubs but this has been my home for the last five years," Fonte said.
"I've been successful here
I've had so many promotions and so many good memories and why would you want to change something that's been so good for you?
"Yes we have lost a few good players and we lost a manager.
"But we brought in another great manager and so far he has been great for us so I still think we have enough quality in the team to do well."
Source : PA
Source: PA