The Ghana international is wanted by the Premier League's biggest clubs and his contract carries a £65m buyout clause which can be triggered between January 1-10 during next month's winter transfer window.
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BBC Sport says Bournemouth management are urging Semenyo to stay for the season and are even prepared to take a loss on the price of his clause and sell him for less over the summer.
There is also talk of the two parties signing a contract which would guarantee Semenyo's sale after the World Cup.
Watching developments are Manchester United and Tottenham, which are both exploring the prospect of paying the player's clause next month.