Both Manchester United and Liverpool made attempts for Semenyo last summer and remain keen leading up to the January market.
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The Mirror says Manchester City are also interested as manager Pep Guardiola seeks an extra attacking addition. Significantly, Semenyo won't be Cup-tied from European football over the second-half of the season.
The Ghana international penned a new deal at the start of the season to 2030 and has insisted he won't agitate for a move away.
But Bournemouth are said to be willing to sell Semenyo in 2026 if an offer of £70m or more arrives for the goalscoring flanker.