Southampton chairman Ralph Krueger says no action has been taken against Morgan Schneiderlin.
The France midfielder hit out at the club on Twitter after a move to Tottenham was blocked last week.
"We're not the kind of club that right off the bat is going to overreact," Krueger told PA Sport.
"The fact of the matter is there is a strategy in place and that we clearly have Morgan and Jay [Rodriguez] in the centre, as a core players of building this squad going forwards. That is our strategy and we're going to stick with it. We are now on a building and not in a reducing phase.
"Very clearly we don't communicate with our players in the public, so he was clearly informed of the fact we were not going to sell him. Immediately after that I communicated with the media about that and that is how we did it. Then he reacted (on Twitter).
"I think whoever reacts in certain ways, there is passion involved here and circumstances."
Asked if Schneiderlin had been reprimanded for his Twitter post, Krueger said: "No, he wasn't. I think that there's situations that evolve where people can be emotional.
"You shouldn't, as a club, take everything personally and we didn't take that personally."
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