Brendan Rodgers' side head to Dean Court searching for a change of fortunes following a 1-1 draw against Basel last week that dumped the club out of the UEFA Champions League and a 3-0 defeat at arch-rivals Manchester United on Sunday.
Victory over Championship leaders Bournemouth, however, would put Liverpool into the League Cup semi-finals.
And although former Liverpool midfielder Hamann is well aware of Bournemouth's calibre – they are unbeaten since the end of the September – he knows what impact a win could have for everyone concerned at Anfield ahead of this weekend's Premier League clash with Arsenal.
"In a season, sometimes you just need one result and one spark from somewhere then all of a sudden the whole complex of the season and team changes," Hamann told the club's official website.
"It's tough going to a Championship team on any given day, and especially when you go to a team that are top of the league and on a fantastic run.
"It doesn't matter where you are in the league and what's happening - if you are in the last eight of a cup competition, it's always a big game, because this club is about winning trophies.
"You have to be in the Champions League, but you need to win a trophy every now and then. As a club, a team and players, you learn an awful lot about yourself and your team-mates when you play in a quarter-final, semi-final or, hopefully in this case, a final.
"It is an opportunity; I'd rather go to Bournemouth away than Chelsea or Manchester City away, and Liverpool will be favourites. They have just got to get out there.
"If you go to Bournemouth and win the game, then you look forward to the Arsenal game. A week is a long time in football. They just have to keep working hard now, believe in themselves, get a result on Wednesday and then move on to Arsenal."