Midfield linchpin Schneiderlin has again been linked with a move away from St Mary's, with Arsenal and Tottenham prepared to renew interest next month.
The France midfielder was persuaded not to leave Southampton amid a summer exodus and new boss Koeman has since guided the south coast club to fifth in the Premier League.
Koeman has pledged Saints will not let anyone leave in next month's transfer window, while also eyeing two additions.
"We will sell nobody in January," said Koeman ahead of Saturday's Premier League trip to Burnley.
"Morgan's attitude is fantastic - everybody knows that he had a difficult time in the summer, but finally he accepted his situation and he's doing his best and looking forward to returning to playing."
Schneiderlin will miss Saturday's Turf Moor clash as he continues to battle a groin problem, but could make a return in Tuesday's Capital One Cup match at Sheffield United.
Fit-again Toby Alderweireld will ease Saints' midfield injury glut after being cleared to return for the Burnley battle, while James Ward-Prowse has almost beaten his two-month ankle problem.
Koeman admitted losing Maya Yoshida and Sadio Mane to international tournaments in January could prompt him to dip into the transfer market.
"If everybody's available we don't need somebody," said Koeman.
"But we will lose two players in January to different tournaments: Mane will go to the African (Nations) Cup and Yoshida will go to the Asian tournament.
"That means two players less - maybe for that we need some players, but we have to talk about that inside and make decisions.
"But I think we need one or two players."
Southampton stepped into a testing festive fixture glut sitting second in the table, only to lose three straight games to Manchester City, Arsenal and Manchester United.
The December acid test has hit hard, but Koeman still believes his side can chase Europa League qualification.
"I think so," said Koeman, when asked whether the Europa League was now the target.
"Okay we're always trying for the maximum, but we have to understand our situation.
"We have to be realistic, and maybe that's the target for this season.
"The way of playing is everything .We must keep believing in that, but maybe that's (the Europa League) the realistic situation for our team.
"We can play good, attractive football, but only winning games brings confidence."
While Jack Cork remains sidelined with ankle trouble, Koeman admitted the impending return of Alderweireld, Ward-Prowse and Schneiderlin could provide a timely boost.
"James Ward-Prowse is back in training with the group," said Koeman.
"He needs more time but he will be in the squad for the two games, because we will stay over after Saturday to prepare for the Sheffield game.
"He's one of the 22 players that will travel.
"Morgan, I don't expect him back this weekend, but he will travel with the group, because we hope he will be fit for Tuesday.
"Toby trained normally today, and he will be fit for the weekend."
Source : PA