The Saints were thought to have been preparing a January raid for the Galatasaray star, who is reportedly unhappy in Turkey.
Sneijder, 30, who has made 19 appearances this term and netted four goals, has the same agent as Koeman - with the Dutch stars both being represented by Guido Albers.
However, any move by Koeman to bring the talented playmaker to the south coast could be thwarted by the high-earning Dutch international’s wage demands.
Speaking ahead of the visit of Roberto Martinez's Everton side on Saturday, Koeman said: "I'm interested, but I know we can't pay him.
“There's nothing in it, and I know that because his agent is my agent.”