Italian football website Tuttomercatoweb, as quoted by the Daily Express, is reporting that the Reds are weighing up a potential swoop to sign the 23-year-old shot stopper.
The same article states that Liverpool FC are ready to offer 30 million euros (£26.3m) for the Lazio number one goalkeeper in the 2018 summer transfer window.
According to the same story, Lazio would be reluctant to sell Strakosha given the Albania goalkeeper has four years to run on his current deal with the Rome outfit.
Liverpool FC have been regularly linked with AS Roma shot stopper Alisson Becker over the past few months but the Champions League semi-finalists could price the Reds out of a deal.
The Merseyside outfit have also been touted with an interest in Stoke City goalkeeper Jack Butland after the Potters were relegated to the Championship.
Liverpool FC are thought to be ready to upgrade Loris Karius and Simon Mignolet after both goalkeepers struggled at various points throughout the season.
Karius made two mistakes in the Champions League final to help Real Madrid ease to a 3-1 win over Liverpool FC in the European Cup final in Kiev last weekend.
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