The manager did, however, admit that he cannot categorically rule out new faces at St Mary's.
The Saints were linked with a move for Porto winger Juan Quintero this week, with the Daily Mail claiming that they had sent scouts to watch the Colombian turn out for Rennes, where he is on loan, against PSG.
It was thought that Koeman would make a move for the 22-year-old in January, in an effort to bolster his squad, but the Dutchman has all but ruled out any potential signings arriving in the winter window.
“I’m very happy with the team and the players that we have,” he told saintsfc.co.uk.
“I can’t say 100% because it’s football and it depends on a lot of things, but normally new players don’t arrive in January.”
Given the quality players that Southampton have lost in the last two seasons, it is fair to suggest that they still need to add recruits to bolster their squad.
Koeman is working with a relatively small unit this season, with injuries having shown how thin his options are in recent weeks.
However, that has given the youth players more of a chance to impress, with James Ward Prowse in particular having upped his game this season, and the Dutch boss may be convinced to keep turning to youth rather than sign new players.