The Reds have endured a tricky start to their Premier League campaign and sit seven points behind the current frontrunners Manchester City and Manchester United after seven games.
Liverpool host old rivals United on Saturday and ahead of the clash against the Red Devils at Anfield, Purslow has publicly backed Klopp and feels the German is doing a great job given the resources available to him.
He said: "He is perfect for Liverpool. It is an innately difficult project, to compete with less money.
"I think most Liverpool fans would feel that the team began under Brendan Rodgers with a very new, highly attacking, attractive way of football.
"There were question marks about them defensively and Jurgen hasn't addressed those completely but, in my opinion, the owners know exactly what the job description is. He is the right man for the job and that's going to take five years, not two years."