Talks have now commenced between the two clubs for the young attacking midfielder.
City boss Pep Guardiola has approved the move, with the Catalan eager to bring Cherki to Manchester this summer.
The Daily Mail says OL want €50m to sell Cherki, though are likely to soften their stance with the player demanding a transfer.
"I don't know," he said last month when asked about his future with OL. "In any case, I know I've given my all for the club. I've done everything I could for Lyon, because it's a club I'll never forget, one that will always be in my heart.
"I stayed when a lot of players left. Today, I have no regrets. Whatever happens, I'll give my all to the last minute for the club. I've only got Lyon on my mind, and I'd never call on anyone else."