The Ghana international's free-scoring form over the past has brought him to the attention of Manchester United, Liverpool and Manchester City.
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United had an offer for Semenyo rejected by the Cherries over, which subsequently secured the attacker to a new deal through to 2030.
BBC Sport says the new contract carries a buyout clause set at £65m which can be triggered in the first two weeks of the January market.
Semenyo has six goals and three assists in 11 Premier League appearances so far this season.