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The Dutch forward was heavily linked with a move to Barcelona prior to the 2020-2021 season, speculation that mounted as Los Cules are coached by his ex-Netherlands boss Ronald Koeman.
With Depay out of contract at the end of June, rumours continue to circle that Barca may reignite its interest in the former Manchester United man.
Depay has been influential for Lyon this season, contributing 15 goals and nine assists from 30 appearances in all competitions.
He has a big-chance conversion rate of 61.11 per cent, while he has created 77 chances for team-mates – 16 of which are Opta-defined big chances.
Lyon sits third in Ligue 1, level on 60 points with PSG and three adrift of leader Lille. Aulas hopes that domestic success may convince Depay to reject overtures from elsewhere.
"For Memphis, I dream that he accepts our proposal, which is still relevant," he said.
"He brings so much, he has been directly involved in 23 league goals this season. The offer will stay there and, if we are champions, why not?"