The Catalan club were eager to sign the all action midfielder in the summer after a long term injury to Gavi.
However, Sport states that they do not have the funds to secure Onana in the near future.
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The likes of Manchester United and Arsenal are interested, while Everton will only sell for a mega fee.
Onana may be tempted by a move to Barca, but would have to run down his contract in the next few years to have any chance of making that move happen.
Barca have well documented financial issues that mean big money transfers are not on the cards.