The French midfielder is unsettled at St Mary's Stadium after being told that he will not be allowed to follow five other key players out of the club this summer.
Ex-Saints boss Mauricio Pochettino is reportedly keen to bring the 24-year-old to Tottenham Hotspur, but Koeman has reiterated that he is not for sale and revealed that Schneiderlin has been preparing for the trip to Anfield with the rest of the squad.
"He had a very good week of training sessions," Koeman told reporters. "We know the situation.
"Last week he wasn't in shape to play, he had a very good week of sessions and that decision will be taken tomorrow - he is not for sale."