The Ghana international is producing career best form for the Cherries this season.
The Mirror says Liverpool and Newcastle are showing interest in the 25-year-old.
Bournemouth are demanding £50m for their key player this month.
However, there could be a possible swap deal with Liverpool as Bournemouth are keen on Ben Doak, who is currently on-loan with Middlesbrough.
Semenyo's contract with Bournemouth runs until the summer of 2029.