Schneiderlin, 24, has been linked to Tottenham but Saints chairman Ralph Krueger has said he is not for sale.
The French midfielder wrote on Twitter: "Six years of an amazing journey #saintsfc destroyed in one hour!"
Koeman said: "He is a player of Southampton and will continue to be."
Southampton have already sold five players this summer but Krueger told BBC Radio Solent on Wednesday that Schneiderlin and injured forward Jay Rodriguez would not be leaving St Mary's.
Koeman has warned the Schneiderlin of his future conduct following his comments on social medal and said he expected him to return to the side for the pre-season game against Bayer Leverkusen on 9 August.
"He is OK, he will play next week," Koeman told BBC Radio Solent.
"I spoke with him about that tweet. Always you have to keep that type of information inside and we spoke about that and his situation."
Koeman also said the club were close to signing three new players as they look to add to new recruits Dusan Tadic, Graziano Pelle and Ryan Bertrand.
"We hope to do that this weekend and then we have two weeks still to prepare for the Liverpool game," he added.
The Dutchman hinted that club record-signing Dani Osvaldo could be sold in a swap deal for Inter Milan's Saphir Taider.
"We are looking for the best for Osvaldo and the best for the club," he said.
"Taider brings quality and we need that. We need competition in the squad as well and that will be good."
Southampton manager Ronald Koeman has reiterated Morgan Schneiderlin will not be leaving the club and has warned the midfielder of his conduct following his midweek outburst on Twitter.