Sport says Barcelona are hoping to take advantage of Lacazette's contract saga by adding the Frenchman for nothing.
Arsenal have allowed the forward to run down his deal meaning he can walk away from the Emirates this summer.
Barca are considering a swoop, which would reunite the Arsenal man with Pierre-Emerick Aubameyang.
Barca's president, Joan Laporta, has made it clear they will not break the bank to bring in new faces.
He told Mundo Deportivo: "I insist, I will not talk about specific players but I can tell you that we will not carry out any operation that puts the institution at risk."
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