The Dutch international is being linked with a move away from Feyenoord this summer.
Now, another former Koeman favourite at the Rotterdam club has cast doubt on his future with the Eredivisie side.
"I swear to you, that at this time, there is nothing [regarding ongoing transfer talks].
"[However] it is clear that, if you play every week with better players, you also get better. I do not want to do the Eredivisie a disservice, but everyone knows that there is a step higher in the world."
Clasie, who has been dubbed the 'Dutch Xavi', is currently captain of Feyenorrd and a regular Dutch international.
The Mirror reported just yesterday that Southampton were keen on signing the 23-year-old, valued at £10 million, as a potential replacement for Morgan Schneiderlin - should the Frenchman depart this summer.
Clasie was a regular under Koeman at the De Kuip Stadium and he knows his game well, so he would love to bring him into the club.
Koeman has had success with his knowledge of the Dutch market already, with Dusan Tadic, Graziano Pelle and Toby Alderweireld, Eljero Elia and Filip Djuricic all arriving at the club with previous in the Eredivisie.