Netherlands international Depay joined Lyon from Manchester United in January 2017 for a reported €16 million ($27.3 million) and has been a key player for the Ligue 1 side.
After a difficult period in England, scoring just twice in 33 Premier League matches, Depay has rediscovered his form since moving to France, netting 43 times from 102 top-flight appearances.
He began the 2019-2020 campaign in fine form before a serious knee injury had seemingly ended his season, though the suspension caused by the coronavirus pandemic may yet mean Depay can play a part in Lyon's run-in.
Throughout Depay's time in Lyon, he has been a source of transfer speculation and, with a little more than a year left on his contract, rumours could intensify when he returns to fitness.
Aulas, though, assured supporters the club will do everything in their power to keep him with Les Gones.
"There is no break [in the relationship]," Aulas told the club's official TV station. "We talk to his agents, I chat with him, and we will have the opportunity to meet him.
"We will do everything to evoke an extension. All the authorities in Lyon are in favour of extending his contract.
"We are working on it a lot. I have a lot of exchanges with Memphis, Rudi [Garcia, Lyon's coach] too and Juni [Juninho Pernambucano, Lyon sporting director]. Not daily, but regularly.
"We made him a certain number of proposals, which he did not accept. He was waiting to be able to resume playing. He had imagined being able to play the Euros with Netherlands, then there was this injury. He recovered faster, but for the moment we have not agreed."