Liverpool have had an interest in Sanchez for a while now, who is also wanted by Juventus, Atletico Madrid, Arsenal and Manchester United.
The £25million 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.
The Catalonian club is in a rebuilding phase with Carles Puyol, Xavi and Victor Valdes all leaving, while Dani Alves may follow.
They want an inspirational striker but do not have the spending power of fierce rivals Real Madrid.
Instead the Nou Camp outfit will use talent like Sanchez, 25, to bridge the financial gap.
Napoli’s hitman Gonzalo Higuain is also on Barcelona’s radar but the Italians have already warned he will cost £55m if they pursue their interest in the Argentina ace.
Liverpool will resist bids for Suarez but his comments after Thursday night’s defeat of England will 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.”
Real Madrid also remain keen on Suarez and will challenge Barca for his signature.
Written by Steve Milne
