The Saints boss is convinced the France international will not leave the club in the transfer window and has praised his attitude in the wake of transfer speculation
Goal understands Tottenham are planning a €20m bid for the France international with manager Mauricio Pochettino determined to land his former players before the close of the transfer window.
However, Koeman has reiterated his desire to keep Schneiderlin, following the departures of Luke Shaw, Adam Lallana, Calum Chambers, Rickie Lambert and Dejan Lovren, and praised his attitude.
"No, for us that [situation] is away [gone]," he told reporters. "The rumours about him are away. He played a fantastic match against Liverpool [last Sunday] and how he has acted is fantastic.
"He has to continue to show his qualities like on Sunday and we are happy to have him in the squad.
"It doesn't depend on offers. He will stay at Southampton."
Koeman also spoke in some length about new signing Dusan Tadic – who enjoyed an encouraging debut in the 2-1 defeat at Liverpool last weekend – and youngster James Ward-Prowse, highlighting the impact both made at Anfield in Southampton's Premier League opener.
"Tadic played well," he continued. "He played the assist for our goal. He is a quality player.
"He and [Graziano] Pelle have to realise, though, it is not the Dutch league. It is high tempo during the whole match.
"Sometimes they have a problem with that, but little-by-little they will show why we signed these players."
Koeman added about Ward-Prowse: "He is a great talent. I hope and I think he will have a great future.
"He has already played a lot in the first team and is a boy from the academy. He is a great player.
"He has a good feel for good positions in the midfield and he is important for set pieces. I told him I really like him this week. He has a great future."
Ward-Prowse has been compared with England legend David Beckham, but Koeman said: "Don't put names like that. It will make a lot of pressure for him.
"Of course, Beckham was a great player and it is difficult to compare players to him, but I believe in his [Ward-Prowse's] qualities. If he is showing these abilities now then he will have a great future."