Reports in the British press suggested Koeman was contemplating an audacious bid to bring his fellow Dutchman, who has also been linked with Manchester United, to the St Mary's Stadium in January.
Koeman concedes Sneijder is a player that interests him, but believes a move for the former Real Madrid and Inter man is not feasible.
"I am interested," he said. "But we can't pay him.
"I know that because his agent is my agent."
Southampton face Everton in the Premier League on Saturday aiming to arrest a run of five straight defeats in all competitions.
Doing so will not be easy considering Victor Wanyama, Morgan Schneiderlin and Florin Gardos are all suspended.
Koeman also revealed that Dusan Tadic will play no part due to fatigue, while Graziano Pelle and Steven Davis could miss out for a similar reason.
"We have three players suspended. Gardos, Morgan and Victor," he added.
"We have some long injures like Jay Rodriguez, Sam Gallagher and Jack Cork. Dusan Tadic will not be available for this Saturday and two players are doubtful - Steven Davis and Graziano Pelle.
"Tadic is tiredness built up by playing a lot and that's the difference between playing outside and inside the Premier League.
"They are players who need normally a break. They don't have a break and it's the same for Steven Davis and Graziano Pelle.
"You have to understand we have more international players than the club ever has in the past. You have to get used to that programme.
"That's a difficulty for us and a new situation. It's a lot of changes in the team, that's part of football and it's a problem."
