The £25million-rates Chilean has been excellent in the World Cup and the Nou Camp giants want Liverpool to accept a package of £56m plus Sanchez for Suarez.
Suarez's comments after Thursday night's defeat of England are being tipped to make it difficult for him to play in the Premier League next season.
"People in England laughed about my attitude over the last few years," he said.
"I want to see what they think now. I have dreamed of this moment."
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