Those hopes may be slim, but the Reds are only three points off the top six and if they can find form in the run-in they can possibly chase down the top four.
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Jurgen Klopp's side ended a four-game winless run in the Premier League with an emphatic victory against Leeds last time out.
And by building on that win at Anfield this weekend, it could lead to a late charge for a European spot.
They face Steve Cooper's Forest who are fighting for their lives at the bottom of the table with every point being crucial in the relegation battle.
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Liverpool vs Nottingham Forest: talkSPORT coverage
This Premier League clash will take place on Saturday, April 22.
Kick-off at Anfield is scheduled for 3pm.
talkSPORT 2 will have live coverage of the game presented by Dan Windle.
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Commentary will then come from Ian Danter and former Arsenal winger Perry Groves.
To tune in to talkSPORT or talkSPORT 2 through the website, click HERE for the live stream.
You can also listen via the talkSPORT app, on DAB digital radio, through your smart speaker and on 1089 or 1053 AM.
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Liverpool vs Nottingham Forest: Team news
Luis Diaz made his long-awaited return to action against Leeds last time out and will be in the Liverpool squad again.
However, Naby Keita and Stefan Bajcetic will remain on the sidelines.
As for Forest, Chris Wood is out of action until the end of the season with Taiwo Awoniyi likely to lead the line with Brennan Johnson.
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Cheikhou Kouyate, Serge Aurier and Gustavo Scarpa are expected to be out once again.
Ryan Yates, Willy Boly, Omar Richard, Giulian Biancone and Dean Henderson round off a long list of injured players for Forest.
Liverpool vs Nottingham Forest: What has been said?
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Liverpool have had a very poor season by their standards but after thrashing Leeds, Klopp is keen for his side to use that to end the campaign strongly.
"The challenge now is to build on this," he said. "I don't know where it will lead to. It's super important what happens from now on because if it goes on, there will be a next season.
"I have no clue where we will end up this season, it depends massively on other teams around us who can win all their games. We can't do much about that.
"We played a really bad season but some things are not really to explain and some definitely are and are not acceptable. We have to understand what is possible.
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"I just want us to play top football and win games and we will see where we end up."
Liverpool vs Nottingham Forest: Match facts
Against Leeds last time out, Trent Alexander-Arnold recorded his 50th Premier League assist, becoming the third-youngest player to hit that total in the competition (24 years, 192 days), after Cesc Fàbregas (22y 145d) and Wayne Rooney (24y 84d). Alexander-Arnold has three assists in his last two league matches, after having only assisted two in his first 27 this season beforehand.
Mohamed Salah has been involved in nine goals in his last five home games for Liverpool in all competitions (6 goals, 3 assists), scoring in all five matches. The Egyptian himself was the last Liverpool player to score in six in a row at Anfield, doing so in March 2018.
Away from home in the Premier League this season, Nottingham Forest have the fewest points (6), joint-fewest wins (1), fewest goals scored (5), worst goal difference (-31) and second highest number of goals conceded (36).
Liverpool have scored 39% of their Premier League goals this season (22/56) in their wins over Bournemouth in August (9-0), Man Utd in March (7-0) and Leeds last time out (6-1). In those three matches, they scored 13.2 more goals than their expected goals tally (22 from 8.8 xG), whereas in in all other Premier League games this season, they have underperformed their xG by 12.7 (34 goals from 46.7 xG).
Nottingham Forest are without a clean sheet in their last 10 Premier League games. In fact, Forest are winless in all 24 league games in which they've conceded this season (D8 L16), with all six of their victories being to nil.
Nottingham Forest are winless in their last 10 Premier League games (D3 L7), their longest such streak since a run of 19 between September 1998 and January 1999.
Liverpool have lost just one of their last 37 Premier League home games (W27 D9), a 2-1 loss against Leeds in October. They've also only failed to score in one of these 37 games, a goalless draw with Chelsea in January.
Only two promoted teams have ever done the Premier League double over Liverpool - Newcastle United in 1993-94 and Blackpool in 2010-11.
Nottingham Forest won the reverse fixture against Liverpool 1-0 in October - only twice before have they ever done the league double over the Reds, doing so in 1910-11 and 1962-63.
Liverpool are unbeaten in their last 23 home league games against Nottingham Forest (W18 D5), since a 2-0 loss in February 1969.
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