The 22-year-old enjoyed a breakthrough campaign last year, earning 10 goals and 14 assists, building up a strong partnership with Andi Weimann.
Semenyo has yet to make an appearance for the Robins this season after sustaining a shin injury whilst on international duty with Ghana in June.
A report from the DailyMail claims that Patrick Viera’s Crystal Palace are willing to pay £12m for Semenyo. Palace have looked to the Championship before for a number of players, signing the likes of Michael Olise, Luke Plange and Eberechi Eze.
Palace aren’t the only top-flight team interested however, Bournemouth have been long-term suitors whilst Everton are now keen on the player. Scottish Premiership giants Celtic have also been keeping close tabs and have scouted him at games last season.
The Mail adds that City want an initial £15m for the one-time Ghana international and would expect add ons which would make a deal worthwhile.
Last week Steve Lansdown, who opened up on his desire to sell his shares in the club, said City were not in a position that they needed to sell their star players such as Semenyo and star-boy Alex Scott, who is wanted by Manchester United, Tottenham Hotspur and Leeds United.
He did however admit that he wouldn’t stand in their way if any Premier League clubs came in for them and matched their valuation.
Lansdown said to BBC Radio Bristol: "The first thing you have to have is an offer for them which we haven’t got. How do we retain them? "They’re under contract. Antoine’s got two years, Alex has got three and we don’t need to sell them and we don’t want to sell them.
“So like all these things you have to make offers to make you change your mind because that money can be reinvested to bolster the rest of the squad.
"I think the transfer market is only with the Premier League sides. They have the capital to do it and the owners who can put the money in to do something but strictly speaking, I don’t think that’s there anymore.
"Why would Alex or Antoine want to go to someone else in the Championship? They have fantastic facilities here, it’s a great club to be a part of, great team-mates and a progression that they can see in their own careers but when a Premier League club comes in for them that’s when it’s difficult to turn down and I wouldn’t stand in their way."
As to where the reported clubs are at in the transfer market, Palace are in need of a striker after selling Christian Benteke to Major League Soccer outfit DC United, who are managed by Wayne Rooney.
Everton meanwhile could stump up the funds quickly because of midfielder Anthony Gordon’s reported £50m sale to Chelsea, which would be on top of what they received for Brazilian forward Richarlison.
England international striker Dominic Calvert-Lewin is currently sidelined through injury and so Semenyo could be a genuine first-team contender.
In City’s case, they have coped without Semenyo as Andi Weimann has continued his scoring streak from last season, scoring in all four of their matches this season.
He has continued to partner Chris Martin, whilst academy graduates Sam Bell and Tommy Conway have both been rewarded with new contracts this summer.