Silva, 31, is one of several key figures set to leave Man City at the end of the season as the Premier League side enter their post-Pep Guardiola era.
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While Vlahovic, 26, is also likely to become a free agent as contract talks with Juventus continue to stall.
According to journalist Sique Rodriguez, both players have been offered to Barcelona, but the La Liga champions aren’t interested.
It’s understood that Hansi Flick’s side are happy with their midfield, so don’t feel the need to add Silva to their ranks.
As for Vlahovic, while Barcelona are looking to sign a new striker, he isn’t their priority, and they are instead looking at Julian Alvarez and Joao Pedro.