The Daily Express says Mbeumo could be considered by Liverpool if Mohamed Salah is sold this summer.
Brentford is involved in the relegation battle and in the event of going down, Mbeumo could be available relatively cheaply.
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The winger has a contract with the London club until the summer of 2026 with an option for another year.
Brentford signed Mbeumo from French Troyes in the summer of 2019.
He has managed to score 48 goals and 40 assists in a total of 190 competitive matches for Brentford.