"We don't want anybody to be here who doesn't feel they can grow in the role that they have," said Krueger, who was speaking at the unveiling of Southampton's seven-year sponsorship deal with the kit manufacturer Under Armour.
"That begins with our leader on the first team and that's Ronald. If it's right for him and it's right for us and everybody finds a natural way, that's going to be best for Southampton."
The club sold Adam Lallana, Rickie Lambert, Luke Shaw, Dejan Lovren and Calum Chambers two years ago with Morgan Schneiderlin and Nathaniel Clyne exiting last year.
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Krueger, though, did not expect such high-profile departures in the July-August transfer window and was also optimistic that Koeman, who has more than a year left on his contract, would stay on.
"This summer we have a different comfort zone, and the main reason is that we're maturing as a club," he said.
"Players can see that growth and they want to be a part of it now instead of thinking that over the fence is better than here.
"That applies to Ronald Koeman as well, and our conversations with him have been excellent."
(Reporting by Simon Jennings in Bengaluru. Editing by Patrick Johnston)
