Indeed, the South Coast club bought Virgil van Dijk from Celtic last summer but Koeman says he wasn't entirely convinced by the level at which his compatriot was playing.
In the end, he admits he was convinced by Van Dijk's experience in the Champions League.
"It makes it a little more tricky but he had experience of playing against Barcelona in the Champions League, so in the end there was no doubt about it."
Koeman did sign Van Dijk, of course, and the rest is history.
The Dutchman has been superb for Southampton, both in a defensive and attacking sense, while Celtic's defence has understandably not been the same without him.
Southampton currently sit seventh in the Premier League, five points off fifth and seven off the top four.
The Bhoys, meanwhile, are one point clear at the top of the Scottish Premiership, although they do have a game in hand over Aberdeen.