The France international was vocal with his desire to leave the club following interest from Tottenham but his manager insists he is now happy to stay at St. Mary's
The France international has been a target for Tottenham throughout the summer, with Goal understanding a £17 million bid was planned earlier in the window, although Mauricio Pochettino is now closing in on the signing of Montpellier midfielder Benjamin Stambouli.
Schneiderlin was public in his desire to leave the club in July, but Southampton blocked any sale prompting talk of the player possibly going on strike.
But, following the 24-year-old's man-of-the-match display against West Ham, Koeman spoke of confidence that Schneiderlin would not be sold and dismissed reports of any threat of a strike.
"It's difficult in life to say 100 per cent [if he will stay]. For me, yes, but more like 99 per cent," he told reporters.
"He never said he would go on strike. He's in a comfortable situation now. He's accepted club's decision [not to sell him]."
Meanwhile, West Ham manager Sam Allardyce was frank with his assessment of his players following the loss, but questioned the performane of referee Mike Dean.
"We weren't good enough," he said. "Southampton taught us a lesson, we weren't sharp enough and didn't retain the ball as well as they did, close down as well as they did and gifted them two goals. As much as they were in control and on top of the game we've lost two very stupid goals from set-pieces.
"The big problem I had with the corner [for the second goal] was that it was a goal-kick of course. I've had a look at it on the laptop and can the referee see it? Was he blocked and why didn't he make the right decision? Having looked at it from Mike Dean's position he's got it horribly wrong when we don't need it to go against us."