According to L'Equipe, Lyon's president Jean-Michel Aulas was in London on Wednesday and met with Chelsea officials to discuss a deal for Tolisso. He is keen to play in the Champions League and could welcome a move to Chelsea, who sealed their return to Europe's elite club competition by securing the Premier League title this season.
"That was the key when I came to Ajax - play as many [games] as I could, do well, and try to go back to Chelsea".
Juventus have also shown an interest in Tolisso and were reported to be ready to pay £36million for him.
"I think I had a great season but I don't decide to stay at Chelsea or move".
And his performances have apparently not gone unnoticed at Stamford Bridge.
His departure could see Tolisso walk through the door at the club in the summer, who is a highly promising midfield talent.
They are said to view him as an alternative target to Monaco star Tiemoue Bakayoko.
Nemanja Matic and N'Golo Kante have been exceptional in the middle of the park this season, and in their stead, Cesc Fabregas has stepped up to the plate, giving Conte an array of options to choose from.