Spanish journalist Albert Roge claimed the whizkid, 16, has agreed a pre-contract with the Etihad club.
And Gerard Romero later added that City will pay just training fees for the player as his deal runs out at the end of the season.
Bernabe joined Barca from Catalan rivals Espanyol and Nou Camp chiefs will be bitterly disappointed to lose another prospect.
City have former Barcelona director of football Txiki Begiristain working behind the scenes to develop their own academy.
By investing heavily in facilities and bringing in young talent from all over Europe the hope is to eventually rival Barca's famous La Masia complex.
Pep Guardiola has a proven track record for bringing through homegrown stars.
And he has handed first-team opportunities to Tosin Adarabioyo, Brahim Diaz, Phil Foden and Oleksandar Zinchenko.
Guardiola has just one year remaining on his deal but Kevin De Bruyne is urging his boss to stay and build a legacy at the Etihad.
SECRETS TO SUCCESS How Pep Guardiola shaped Manchester City into Premier League champions including making stars eat together, relentless working hours and cutting Etihad grass to exactly 23mm
He said: “What we want to do now is continue playing the way we have this season and become even stronger.
“The manager is a big part of that and hopefully these can be his first trophies of many here at City. Everyone knows he’s one of the best coaches in the world.
“To achieve what he has achieved in the game is special and to be part of a group of players led by him can only help us to keep developing. He came in two years ago and changed the way we play.
“That obviously takes time to adapt to but we’ve developed together and this season is a reward for all that work.”
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