Schneiderlin has been heavily linked with a move to Arsenal this summer, while Tottenham have also expressed an interest in the player in the past.
But Express Sport revealed this morning that United had also entered the race for the French international and were eyeing up a £25million bid.
There are contacts and there will be offers.
Idrissa Gueye
Southampton have been quietly preparing for Schneiderlin's departure for some time.
But according to the Daily Mail they are now discussing moves for Feyenoord's Jordy Clasie and Lille's Idrissa Gueye as they whittle their shortlist down to the final few candidates.
Ronald Koeman is a huge fan of Clasie, who he worked with in Holland, but Gueye is also on the Dutchman's radar after catching the eye of Crystal Palace and West Ham.
GETTY
Idrissa Gueye is on Southampton's radar
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Gueye told La Voix du Nord: "There are contacts and there will be offers. I will have to look at it all and decide what suits me best.
"Find the offer that will allow me to grow, to allow me to take new steps to be in line with my ambitions but I feel good at Lille and if I was to stay here, it would not be the end of the world.
"But everyone knows that England has a league that attracts me, even if I am not closing the door on going to other leagues."