Hudson-Odoi's contract expires in June 2020 and, as long as he remains unwilling to discuss an extension, Chelsea are mindful that his value will likely decrease significantly if he is kept at Stamford Bridge until the summer.
Chelsea have been angered by the public nature of Bayern's pursuit, with sporting director Hasan Salihamidzic confirming on Wednesday that the German giants "absolutely want to sign" Hudson-Odoi this month.
"I think that it is not professional because they are talking about a player under contract with Chelsea, so they didn't respect our club", he said.
"It's insane to have a market window of 30 days at this moment of the season", he said.
Who do YOU think we need, Blues?
The Blues looks set to lose experienced midfielder Cesc Fabregas to Monaco soon and Sarri has already stated that he would like to sign a player to replace the Spain global.
"As you know very well I am not in control of the transfer market".
As reported by the club's official website, Sarri said: 'We need to score.
"Then it depends on the club decision".
"I do like Giroud, he is a very good centre-forward".More news: White Sox reach 1-year agreement with outfielder Jon Jay
More news: 'Not for sale' - West Ham oppose Arnautovic's request for China switch
More news: Trump Threatens National Emergency If He Doesn't Get His Border Wall
It appears obvious, though, that the players Sarri wants are a striker and a midfielder. Sevilla and Atletico Madrid have been linked with the Spain striker.
"Of course, if Morata will go to another club we need a replacement, it's normal", Sarri said.
"At the moment, Morata is here".
"Because in this moment in Europe there are 300 players involved in the market and they need to think only to the next match otherwise it's impossible to play".
"I am happy with the player because is improving, improving a lot in the defensive phase".
'That is all he needs to do, he has all the conditions to be a great player, now it is up to him to fight for a place here or try to find more minutes somewhere else.
"Willian for us is really very important".
The Argentine hitman is Maurizio Sarri's preferred target as the Chelsea manager seeks to bring in a new striker into his squad during the January transfer window.
The Blues were beaten 1-0 by Tottenham in the first leg of their Carabao Cup semi-final and have been criticised for their struggles in front of goal.
Sarri said: "We need to solve this problem".