Austria were touted as potential dark horses ahead of the tournament, but languish bottom of Group F on one point after a 2-0 defeat against Hungary and a fortunate 0-0 stalemate with Portugal.
They now need a win against Iceland, who have drawn both their games 1-1, to have a realistic chance of reaching the last 16.
Austria will be second with a victory unless Portugal also prevail against Hungary, in which case Austria would end up behind Hungary on head-to-head and would hope to go through as one of the four best third-placed sides.
For that though, the likes of winger Marko Arnautovic, striker Marc Janko and Bayern Munich's versatile midfielder Alaba will have to show much more attacking menace against Iceland’s disciplined defence.
“David Alaba is a player who has great qualities and you have to consider he has played a lot with Bayern Munich -- he might have played around 2,000 minutes last season,” Koller told a news conference.
“Not a single other player in our squad has played as much. He has outstanding qualities, both technical and in his understanding of the game. He can play in various positions and of course he will play tomorrow."
Koller urged his team's stand-out talent to use his energy more conservatively, rather than chasing every ball, arguing tournament soccer’s hectic schedule made it impossible for players to maintain the same performance level every match.
Centre back Aleksandar Dragovic is available after suspension, while midfielder Zlatko Junuzovic has largely recovered from an ankle injury that forced him to miss the Portugal game.
“We’re very satisfied with his progress. It’s still not clear whether that will be enough for tomorrow,” said Koller.
He urged his players to maintain the effort they showed in neutralising a superior Portugal outfit, but also demanded they be more precise with their passing.
“Our passes have to arrive at a team mate. We have to look for one-on-one situations, try to find the gaps. It has to be our aim to get behind the defence,” added Koller.
In the other group game, Hungary, on four points, will face Portugal, on two.
(Reporting by Matt Smith; Editing by Toby Davis)
