Jean-Michel Aulas remains optimistic the striker will sign a new deal.
He adds that Barca are unable to afford Depay's transfer.
"I've made Depay an irresistible offer to renew. You cannot refuse it in principle. It's a beautiful offer," Lyon's president Jean-Michel Aulas told local newspaper Le Progres.
He added on the striker's future: "Right now, there is nothing impossible. If he doesn't continue with us, we'll adapt."
On Barca's attempts to land the 26-year-old, Aulas stated: "Clearly, Barca's finances cannot allow this transfer."
Depay's current contract with Lyon expires in 2021.
Barca reportedly agreed the personal terms with the Dutchman weeks ago as Ronald Koeman wants his fellow countryman to replace Luis Suarez at Camp Nou.
The Catalans are believed to have agreed on a €25m plus €5m in add-ons transfer fee with Lyon as well.
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