Bayern Munich have offered £13.5m plus add-ons for Callum Hudson-Odoi but Chelsea want at least £22.5m, Sky sources understand.
According to Sky Germany, Borussia Dortmund are also interested in Hudson-Odoi, whose current contract with Chelsea expires in the summer of 2020.
The 18-year-old forward, who joined Chelsea at U8s level, is viewed as one of the best talents in the club's academy and one of the best players the Blues have produced in recent seasons.
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Hudson-Odoi played a key role in England's 2017 Under-17 World Cup victory, appearing in all nine matches and setting up three goals in the 5-2 victory over Spain in the final.
Another member of that victorious England team, Jadon Sancho, has gone on to achieve great success in the Bundesliga since leaving Manchester City to join Dortmund in 2017.
Hudson-Odoi made his debut for Chelsea in January 2018 when he came on as a substitute in an FA Cup over Newcastle. He made three more substitute appearances under Antonio Conte, including one in the Premier League against Bournemouth.
Hudson-Odoi made his first Premier League appearance of the season on Wednesday against Watford when he replaced Pedro in the 43rd minute, but he was withdrawn late in the game after suffering a hamstring injury.
He has featured four times in the Europa League under Maurizio Sarri, starting twice.
Hudson-Odoi scored his first senior goal for Chelsea in a 4-0 win over PAOK in the Champions League last month but afterwards Sarri cautioned that he is not yet ready for the Premier League.
"I don't know if Hudson-Odoi is able for the Premier League at 18, especially in a big team," he said.
"If he's good enough to play in a big team in the Premier League at 18 then he could be the best player in Europe in two years."