Chelsea are willing to allow Callum Hudson-Odoi to run down his contract next season.
The Blues turned down a £22.4million offer from Bayern Munich for the 18-year-old from the Bundesliga champions earlier this week.
But Bayern are not taking no for an answer despite that knockback and their failure to land the England international with much larger bids in the January transfer window.
The size of the new offer is not known but will be well short of the £40m the German giants were willing to pay just a few months ago.
Chelsea are taking a calculated gamble as Hudson-Odoi enters the final year of his contract, says The Sun.
The club is hopeful the player will sign a new five-year deal once a new manager is in place at Stamford Bridge.