Depay is a target for embattled LaLiga giants Barca following the appointment of former Netherlands head coach Ronald Koeman, while Serie A team Roma have also been linked.
Juninho discussed Depay's future at Groupama Stadium amid Barca's pursuit, telling RMC Sport: "We haven't received an official offer from Barca.
"Memphis, before his serious injury, received an offer from the president [Jean-Michel] Aulas to extend his contract, but he wanted to take his time.
"When a young player aged 26 has one year left on their contract and Barca are following him... Memphis is in a strong position."
Netherlands international Depay scored 15 goals in 22 games for Lyon last season despite suffering a ruptured anterior cruciate ligament in December, as the French side reached the Champions League semi-finals.
"If an offer arrives, we will have to think about it," Juninho said. "We could keep him for another year as captain and lose him for free next year. The president could make an effort to extend [his deal], but I think it will be difficult.
"Memphis didn't ask anything from us before going with the national team. He told me he hadn't received any call from Barca."