The Red Devils have been heavily linked with a swoop for the France international midfielder in recent days as Louis van Gaal looks to continue bolstering his squad ahead of his second season in charge at the club.
United were thought to have had a bid in the region of £20m rejected by the south coast club in recent days, with Southampton reported to be holding out for at least £25m.
Now, Southampton boss Koeman has confirmed the Red Devils’ interest in the player, but said that their initial offer for Schneiderlin “wasn’t serious”.
Koeman is quoted as saying by Goal: “A lot of speculation, but two weeks ago we had a bid of Manchester United, it wasn’t enough, it wasn’t serious, and no more bids till today.
“Everybody knows the situation of Morgan. I understand the player – if he can get a big move to a big one [club], I can understand it.
“I hope that if there is any business, that it will be soon because it’s best for the player, best for us, we have to prepare ourselves if we sell the player.
“No, of course I’ve had a lot of meeting with Morgan. I had a meeting last week with Morgan, everybody knows his situation. But it’s important for the player to do a good pre-season. And we will see what happens in the next few days.
“I don’t talk about money, about numbers, it’s not my business, it’s up to the club.”
Arsenal have also been credited with an interest in the midfielder, as the 25-year-old continues to be linked with a move away from Southampton.
Last week, speculation linking the midfielder with a transfer to United gathered pace when the club’s photographer followed the midfielder on Twitter.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news