The club is already being investigated by the Football Association and Premier League over allegations related to youth transfers and financial fair play rules, AFP reported.
European football's governing body UEFA is also looking into potential breaches of the Financial Fair Play, an investigation that could result in City being banned from the Champions League.
A transfer ban for the Premier League champion would come less than a month after Chelsea was hit with the same sanction for 29 breaches of article 19 of FIFA's regulations on the transfer and status of players.
The west London club has already lodged an appeal against that punishment but was told by world governing body FIFA last week that the sanction would not be frozen while the case is being reviewed, as Chelsea had hoped.
FIFA has been investigating City's international transfers for several years, although the club was cleared of breaking the rules when it signed Benjamin Garre from Velez Sarsfield in 2016 just after the Argentine midfielder's 16th birthday.
According to the Sun report, FIFA believes City has crossed the line, though, in regards to its relationship with FC Nordsjaelland and the Right To Dream football academy in Ghana that is also owned by the Danish side's president, Tom Vernon.
Last year, two players from the academy, Sierra Leone's George Davies and Ghanaian Dominic Oduro, told Danish newspaper Jyllands-Posten that they signed for City and played in youth matches before they turned 18.
Both have since left City – Davies now plays in Latvia and Oduro in the US – but FIFA has been investigating their time with the English club.
And that investigation was broadened later in 2018 when a second Danish newspaper, Politiken, published a story that said City had a secret deal with Vernon to have first refusal on the best prospects from Right to Dream.
If true, that would be a breach of the rules preventing the third-party ownership of players, as City could be argued to have undue influence over another club's players.
Neither FIFA nor City were available for comment on Thursday.
City has welcomed the UEFA investigation into allegations that the club tried to circumvent Financial Fair Play regulations, and Blues boss Pep Guardiola said on the issue last week, "I said last season I trust a lot what the club has done because I know them. Hopefully they can solve it as soon as possible."
As well as Chelsea, Spanish trio Atletico Madrid, Barcelona and Real Madrid have all been punished for signing under-age players from abroad in the past.
Real was able to get its ban reduced on appeal to the Court of Arbitration for Sport, an avenue Chelsea will also explore.