Website 90Min is reporting that the Reds are interested in a potential deal to sign the England international in the summer transfer window.
The same article states that the 26-year-old Englishman has a contract with Premier League side Burnley until 2020.
According to the same story, Burnley would be prepared to sell Pope for a transfer fee in the region of £15m in the current transfer market.
Jurgen Klopp is thought to approve of the price tag and feels Pope would represent bette value for money than some of their other summer targets.
Liverpool FC have been heavily linked with a move to sign AS Roma goalkeeper Alisson Becker over the past few months.
The Real Madrid target is thought to have a price tag in excess of £80m, which would force Liverpool FC to smash their transfer record.
The Italian side are thought to be reluctant to sell Alisson to Liverpool FC after the Reds recruited Premier League sensation Mohamed Salah from AS Roma in a £39m deal last summer.
Liverpool FC lost 3-1 to Real Madrid in the Champions League final last month.
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