City have agreed to meet Semenyo's £65m release clause, which must be activated by 10 January.
The Bournemouth winger is due to have his medical after the Cherries' game against Tottenham on Wednesday (19:30 GMT).
Despite interest from five clubs including Chelsea, Liverpool, Manchester United and Tottenham, City are the only team to have made formal contact with Bournemouth.
"I think it could be the last game," said Cherries manager Andoni Iraola before his side host Spurs.
"That is my personal opinion, but there is nothing agreed and nothing signed. It is my personal opinion as I understand the market and the noise but there is nothing agreed right now. He, right now, is our player and I hope it continues."
Semenyo has scored nine goals and provided three assists for Bournemouth this season.
Iraola also added that the Ghana international is "almost impossible to replace".
