Striker Long joined from Hull City on Thursday, for a fee widely reported to be in the region of £12million.
Schneiderlin, on the other hand, has been heavily linked with a move away from St Mary's Stadium, with a Tottenham touted as the most likely destination for the France international.
Liverpool have shorn Southampton of three of their key players from last season with Rickie Lambert, Adam Lallana and Dejan Lovren all completing moves to Anfield.
After Schneiderlin hinted that he would like to join former Southampton manager Mauricio Pochettino at Tottenham, Koeman left the midfielder out of Saturday's 1-0 friendly defeat to Bayer Leverkusen claiming he was not in the right mental state to play.
But in a press conference on Friday, Koeman was giving little away as to whether either Schneiderlin or Long would start at Anfield.
"He [Schneiderlin] has had a very good week of training sessions," he said.
"Last week he wasn't in shape to play. He's had a good week in training and that decision will be taken tomorrow.
"We are very happy that we signed Long because from the beginning of pre-season he was a target on our list to bring in.
"We lost some good players but brought in new ones. Long is an important player, we need that type of striker because we don't have that type in our squad.
"Tomorrow we have our last session and we'll decide on that [Long's selection] tomorrow."
