The 19-year-old made his first Premier League start since February as Chelsea thumped Crystal Palace 4-0 at Stamford Bridge on Saturday.
Hudson-Odoi is understood to favour staying at Chelsea, and Lampard has reiterated his desire to keep the young star in west London.
But the 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 powerhouses 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.
“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.”
Bayern Munich manager Hansi Flick mentioned Hudson-Odoi at his pre-match news conference, admitting that the club was thinking about signing him.
“I don’t know what will happen. He’s one of the best talents on his position and can play as a winger and even as a striker. That’s why Bayern Munich is thinking about him.”
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