Schneiderlin is a target for former Saints boss Mauricio Pochettino, who wants to take the 24-year-old with him to Tottenham Hotspur.
It has been of a summer of sales on the south coast as Adam Lallana, Rickie Lambert and Dejan Lovren have all moved to Sunday's opponents Liverpool, while Luke Shaw signed for Manchester United and Arsenal took Calum Chambers to the Emirates Stadium.
But despite Schneiderlin being keen on a move to Spurs, Koeman is confident he can keep hold of the players.
"He had a very good week of training sessions," Koeman said. "We know the situation.
“Last week he wasn't in shape to play, he had a very good week of sessions and that decision will be taken tomorrow - he is not for sale."
Koeman faces a difficult task in reproducing the performance of Southampton last season, in which they finished eighth, after losing so many players in the summer.
But he is confident relegation will not be a concern for the Saints, and hopes to soon a wide midfielder very soon.
"For me, (finishing) eighth to relegation is a lot of positions (to lose)," Koeman said.
"I don't think that will happen - we lost a lot of good football players but brought in some new ones.
"The pre-season was difficult, but it's been difficult for everybody. Until the end of August we can bring in more changes but every team has that problem.
"We are prepared and I believe in the qualities and our ambition and that we can do a good season."
Koeman has started his rebuilding process with the signings of Dusan Tadic, Graziano Pelle and Fraser Forster, combined with loan deals for Ryan Bertrand and Saphir Taider and the £12m acquisition of Shane Long.
The Republic of Ireland striker was brought in from Hull City, with Romania defender Florin Gardos also joining from Steaua Bucharest.
"It was very important because it's a part of the ambition that we have as a club and we have shown that in the last few weeks," he said.
"Shane Long is an important player of the team and we need that type of striker because we didn't have that type of striker in our squad and we are very happy to sign him."