The Athletic's David Ornstein reports that Semenyo's preference is to join Pep Guardiola's side, while the BBC report that the Manchester club are in discussions over the move.
Reports suggested that a number of clubs have already made enquiries over the Ghanaian, who has a £65million release clause in his contract which is active in the first ten days of the transfer window.
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Those clubs are reportedly Manchester United, Spurs, Chelsea and Liverpool, as well as City.
But the Cherries are willing to negotiate with clubs who are willing to let Semenyo stay to the end of the season at Dean Court, according to the BBC.
Nothing formal can be agreed at this stage, with the January transfer window set to open next week.
Semenyo signed a new deal in the summer to keep him at the Vitality Stadium, in which this release clause was included. It is active at the start of the January window, before it becomes active once again in the summer, but at a lower value.
As the clause must be triggered early on in January, it will give the Cherries time to bring in reinforcements to replace the forward, who has scored eight goals so far this season, including two in the past two games.
Andoni Iraola said earlier today in his press conference ahead of the Brentford game that he hopes Semenyo will stay as a very important part of his team - but he admitted that it was beyond his control.