The i reports Liverpool chiefs are ready to bid for Semenyo in the New Year over concerns for Mohamed Salah's form.
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Manchester United are also interested in Semenyo, who is rated at £75m by the Cherries.
The Ghana international signed a new five-year contract with Bournemouth in July amid claims the deal carries a buyout clause, though figure is unknown.
Liverpool did business with Bournemouth over the summer for fullback Milos Kerkez and also count on sporting director Richard Hughes, who used to work at Dean Court.
