De Bruyne’s time at Stamford Bridge could be short-lived, as the Belgium international midfielder is not happy in London.
Wolfsburg confirmed their intention to make a bid for the 22-year-old and Juventus are expected to follow suit.
He spent last season on loan at Werder Bremen and is thought to be worth £6m.
Tuttosport also claims the Bianconeri are keeping an eye on Griezmann, the 22-year-old French forward who last season scored 10 goals in 34 Liga games.
He helped Real Sociedad clinch third place and enter the Champions League, but the club could be tempted to sell in January if they are eliminated in the first round.