The People says Saints see Vilhena as a replacement for contract rebel Jack Cork.
Southampton would rather sell him than risk losing out on any cash for the ex-England Under-21 international.
And they will use the windfall from Cork's exit to make a £4m move for Feyenoord youngster Vilhena.
The midfielder, 20, burst on to the scene four years ago for the Rotterdam club and played extensively for Koeman.
But under new boss Fred Rutter he has found game-time more difficult to come by and the Saints' boss has picked up on that.
Everton are also interested in Vilhena.
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