This latest development comes after the Championship side finally agreed on a fee for the 23-year old goal poacher with the top-flight club on Wednesday, January 25.
A reported figure of around £9 million plus bonuses is said to have been accepted by the Robins after the Cherries saw two offers knocked back last week.
Manager Nigel Pearson admitted in a press conference that Semenyo is now expected to travel down to the south coast for the formalities ahead of putting pen to paper.
“As we stand at the moment, Antoine is in discussions with Bournemouth.
“I can confirm that. But the driver of those types of situations is two clubs agreeing on a fee. That has happened now.
“The club, at some point, will disclose what that is, but not today.
“He’s been given permission to speak to the club and there will be an opportunity for a medical. That’s where we are with that.
“No real further comments on that at the moment.
“The most important fact to recognise at the moment is a fee has been agreed between the two clubs so now there are other factors to wait to see; one being a medical and one being agreeing personal terms,” Pearson told reporters.
Semenyo played for the Black Stars at the 2022 World Cup in Qatar and has scored 20 goals and 22 assists for Bristol City.