Champions League winners Bayern offered Chelsea a deal to take Hudson-Odoi on a season-long loan and then buy the England winger at the end of the campaign.
The Blues are understood to have rejected the big-money offer, with Frank Lampard keen for Hudson-Odoi to stay at Chelsea.
Chelsea boss Lampard has however admitted there is “no definitive answer” on whether the England winger will stay at Stamford Bridge beyond Monday’s transfer deadline.
Hudson-Odoi made his first Premier League start since February as Chelsea thumped Crystal Palace 4-0 at Stamford Bridge on Saturday.
Lampard wants to keep Hudson-Odoi, despite recruiting attacking talents Timo Werner, Hakim Ziyech and Kai Havertz this summer.
But the big-spending Chelsea boss conceded he could never say never when it comes to top-level transfers.
Asked whether Hudson-Odoi will be staying at Chelsea beyond the deadline, Lampard said: “There is no definitive answer. By Monday we will know the answer.
“They (Bayern) might have declared their interest, which is one thing, but as I have just said there in terms of the squad, everything that happens by Monday will be things that are firstly good for us as a club, because Callum is our player, and what Callum wants comes into consideration.
“It has to be right for everybody. At the minute I want Callum as part of my squad, especially with what he offered up today and the second half against West Brom. That is where I am at.”
Hudson-Odoi signed a new, lucrative five-year contract at Chelsea in September 2019, dimming at least in the short-term the admiring glances from Bavarian giants Bayern.
But now the Champions League holders have again shown strong interest in their long-term target.
Lampard hailed Hudson-Odoi’s performance in the comfortable win over Palace, however, which saw Ben Chilwell and Kurt Zouma find the net while Jorginho converted two late penalties.
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“I liked Callum’s performance today, especially in the second half when he was more aggressive and getting at the full-back on the outside,” said Lampard.
“He has the ability on the ball and the pace to do that and put crosses into the box, which he can absolutely do.
“Callum is absolutely part of my plans here. We have Pulisic and Hakim Ziyech injured before Christian came back in today.
“We need options and what Callum showed today and the second half against West Brom is exactly what he needs to show. I am pleased with him.”
Tammy Abraham tried to take Chelsea’s second penalty but was overruled by captain Cesar Azpilicueta, with Jorginho stepping up successfully.
Lampard insisted that was no big issue before praising England left-back Chilwell for a fine Premier League debut for the Blues that reaped a goal and an assist.
“I think Tammy, with maybe his youthful exuberance and the performance that he had in the game, that was very good,” said Lampard.
“He made a bit of a mistake and he wanted to take the penalty.
“We have a designated penalty taker and you saw it with the first penalty. It has been dealt with in the dressing room but no problem either.
“I thought Ben Chilwell was fantastic in his contribution in all senses. I thought he got his goal, assists, his defensive play, his engine to arrive into attack from that left-hand side and he is always ready to join in all the time.
“Getting up and down, considering the injury he has had. With Ben, he is Premier League ready, you could see that with as well as he has done for Leicester. He looked like he had played with us for a long time.”
Palace boss Roy Hodgson was left to lament defensive lapses in a heavy defeat.
“I didn’t think our attacking play was very good, it was nothing like the composure on the ball, passing on the ball that we would have wanted,” said Hodgson.
“It was a bad day for us, but we must give Chelsea some credit, they made it very difficult for us to get that passing game going that we wanted.
“We made too many individual mistakes at the back, and that tends to cost you.”