According to the Daily Mail, Die Roten have tabled a £13million offer for the 18-year-old ahead of the January transfer window.
As a result, the youngster is reportedly keeping an open mind when it comes to his future.
Earlier the Bundesliga champions made a bid in the region of £13.5m which Chelsea rejected immediately.
But Bayern are not the only German club monitoring Hudson-Odoi, with Borussia Dortmund credited with an interest, was well as other Bundesliga sides. He made three more substitute appearances under Antonio Conte, including one in the Premier League against Bournemouth.
Hudson-Odoi is a highly-rated attacker that near enough every Chelsea fan wants to see become a first teamer further down the line and he's been given a taste of the limelight this season.
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If at all Chelsea decide to sell him, they will make sure that they include a buy-back clause in the deal, as per the report.
Kovacic became a Chelsea player shortly after playing a part in his country's surprise run to the final of this summer's FIFA World Cup tournament in Russian Federation.
Should the deal go through the attacker will be the latest English player to join Germany's top clubs, with former Manchester City academy star Jadon Sancho already at Borussia Dortmund and Arsenal youngster Reiss Nelson at Hoffenheim on loan.
Personal terms between Bayern and Hudson-Odoi have yet to be discussed but are not expected to be a problem.