The midfielder, who is a target for Tottenham, has been keen to secure a move away from St Mary's during the transfer window.
However, he has met resistance from Saints, who have continually insisted he will not be sold.
"It is difficult for him, but I said last weekend he should come back on Monday and he understood the situation and he accepted it," said Koeman, who will decide on Saturday involvement Schneiderlin will have at Liverpool.
"It is difficult, but he has to accept and finally he accepts.
"He did very good training sessions (this week) and you see the qualities and then you see why we didn't sell Morgan, because he's a fantastic player."
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