Portugal international Bernardo Silva was heavily linked with a move to the Catalan giants before the start of the season.
The 27-year-old eventually decided to stay at the Etihad and played a key role in Pep Guardiola's charges retaining the Premier League title.
There were reports in Spain recently that Silva's agent Jorge Mendes was informed by the Citizens that he could leave for around £70 million.
However, the Daily Mirror has reported that the Premier League champions have no desire to let the Portuguese attacker leave and will not entertain any bids.
Barcelona have already bolstered their attack with the arrival of Brazilian forward Raphinha, while they have also agreed a deal with Bayern Munich for Bayern Munich striker Robert Lewandowski.
Silva registered 13 goals and seven assists across all competitions and was named in the PFA Team of the Year for the 2021/22 season.