The Reds are enduring a difficult campaign and find themselves eighth in the Premier League and eliminated from the Champions League and FA Cup.
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It's been suggested that Liverpool are gearing up for a summer of change as they look to regroup and challenge for the Premier League title again next term.
With Klopp approaching eight years in charge at Anfield, questions have been asked over his future at the club, particularly given the number of sackings in the Premier League over recent weeks.
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Addressing the German's future, Jordan believes that he'll come under pressure quite quickly if next season gets off to a slow start.
Speaking on White and Jordan, the ex-Crystal Palace chairman said: "I think if Klopp starts next season and gets to October with Liverpool in the same sort of position he'll be gone. I think he'll be gone.
"Everything comes to an end and he's been there for seven years, or eight years in October.
"He's been there a significant period of time and the bulk of the time, certainly after years two and three, he's done a remarkable job and built a remarkable team but these tail-offs that come post-Premier League winning seasons and seasons where they've dominated like last year…"
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Murphy added: "This is the biggest one."
The ex-Liverpool midfielder then went on: "I think that this summer is huge for him [Klopp].
"I'm 100 per cent convinced that he'll get the time to do it and he deserves the opportunity to refresh this squad, get some funds and get some players out.
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"What he's guilty of is relying on the same core group for a long period."