The 23-year-old centre forward has made 26 appearances for Bristol City this season, bagging seven goals while providing two assists.
His performances this season have earned him interest from several Premier League and Championship sides.
Bournemouth submitted a second bid of £10m for Semenyo last week but saw it rejected by Bristol City.
Burnley have maintained their interest in the forward but Vincent Kompany’s side would prefer a move next summer.
It has been claimed that Southampton and Crystal Palace have joined the hunt for the Bristol City star.
And Patrick Vieira’s side are eager to recruit Semenyo as they may lose Wilfried Zaha and Jordan Ayew because their contracts expire at the end of this season.
Southampton are also interested in Semenyo after losing out on Danny Ings to West Ham United and Arnaut Danjuma to Tottenham Hotspur.
Semenyo’s contract expires at the end of this season and Bristol City are yet to trigger the one-year extension in his contract.