Koeman confirmed the Saints had received a bid from Old Trafford for Schneiderlin, who was absent from the club’s first training session of the new season yesterday, but said “it wasn’t serious”.
The Dutchman also said Southampton were hopeful of retaining Toby Alderweireld despite revealing Atletico Madrid, the defender’s parent club, are resisting their move to make his loan deal a permanent one.
“Morgan was ill but he is coming to training tomorrow and he will travel with the rest of the squad to Austria,” said Koeman ahead of Southampton’s pre-season trip.
The Saints play RB Leipzig in the first game of their tour tomorrow.
“He was not feeling well, so he had contact with the doctor and he stayed at home,” Koeman added.
“Two weeks ago we had a big offer from Man United but it wasn’t enough. It wasn’t serious and no more bids today.”
Van Gaal is keen to sign Schneiderlin before United fly out for their pre-season tour of the United States on July 13.
And Koeman is hopeful any deal for the 25-year-old will be concluded in the imminent future.
“Everybody knows the situation of Morgan and if you can get a big move I can understand it,’ Koeman added.
“If there is any business then I hope it will be soon because it is best for the player, best for us and we have to think about ourselves if we sell the player.”
It is believed United’s offer for Schneiderlin was in the region of £20 million (€28.2m).
Asked what fee would persuade Southampton to sell, Koeman added: “I don’t talk about money, about numbers. It is not my business. It is up to the club.”
While Koeman faces up to the prospect of losing Schneiderlin he could also be without the services of Alderweireld this season. Southampton were expecting to complete a £6.8m (€9.6m) deal for Alderweireld after it was understood that Atletico Madrid failed to cancel his buy-out clause in time.
Alderweireld’s performances last season have led to interest from the likes of Tottenham, with reports on Sunday suggesting that they had agreed a deal with the Spanish club.
“Southampton signed an option for the player and Atletico Madrid is trying to take back the option,” said Koeman.
“In our knowledge this was too late and what happened with Tottenham in the middle, I don’t know.
“The player told us he was very happy about Southampton. We mentioned to the player that we would like to continue and that was the case to Altetico Madrid and what happened after, I don’t know.”
Meanwhile, United winger Nani has completed a move to Fenerbahce.
Portugal international Nani leaves Old Trafford permanently after spending last season on loan with former club Sporting Lisbon.
The 28-year-old underwent a medical in Istanbul at the weekend ahead of the move worth a reported £4.25m (€6m).
Nani won four Premier League titles and the Champions League after joining United in 2007 and scored 41 goals in 230 appearances.
He signed a five-year contract in 2013 but then began to fall out of favour and returned to Sporting as part of the deal that took Marcos Rojo in the opposite direction last summer.
He could be back at Old Trafford as early as next month with Fenerbahce potential Champions League qualifying opponents for United.
Elsewhere, Watford have announced the signing of midfielder Etienne Capoue from Tottenham for a club-record fee of £6.3m (€9m).
However, Spurs midfielder Nabil Bentaleb is going nowhere after the 20-year-old signed a new five-year contract with the White Hart Lane club.