Twice a Bundesliga champion with Borussia Dortmund, who he also guided to the 2013 Champions League final, Klopp is yet to win a major trophy at the Anfield club but Purslow said he was under no pressure from the hierarchy.
"He's two years into this job that looked to be perfect for Juergen Klopp," Purslow told Sky Sports.
"There are great similarities between what he achieved at Dortmund, what he was expected to achieve -- which was to compete with an absolute behemoth in Bayern Munich, while spending less money, both on wages and in the transfer market.
"That is the job description at Liverpool."
Purslow said Liverpool's bitter Premier League rivals Manchester United, who visit Anfield on Saturday, earn far more revenue than the Merseyside club, adding that Klopp would need time to repeat his Bundesliga success in England.
"There are revenue differences between Manchester United and Liverpool. Liverpool's are still superb but they are a fraction of Manchester United," he added.
"And yet the Liverpool manager is expected to compete with United and beat them, exactly as Klopp did -- winning two league titles in Germany against Bayern Munich with a fraction of their spending.
"He is perfect for Liverpool. It is an innately difficult project, to compete with less money."
Liverpool, seventh on 12 points, have struggled to convert their goal-scoring opportunities this season but will be fired up for Saturday's fixture against a free-scoring United side, who have won six of seven and drawn just once this campaign.
(Reporting by Shrivathsa Sridhar in Bengaluru)
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