Hudson-Odoi hoped to escalate matters at the end of last week in pursuit of a move to the Bundesliga champions, personally delivering his request for a winter move.
However, he will now have to wait until at least the summer to receive his exit, with Bayern likely to come back for Hudson-Odoi at the end of the season.
The last official offer from the Bundesliga giants was a deal for £35 million ($46m), though after Hudson-Odoi's transfer request the Bavarians were willing to negotiate further.
A move to Bayern is still likely to be Hudson-Odoi's preferred destination next season, but rejecting a sale now provides the Blues with an opportunity to further work to convince the 18-year-old his future is best served by remaining at Stamford Bridge.
Hudson-Odoi's current contract runs out in the summer of 2020 and the winger has thus far rejected all offers by Chelsea to renew it, despite promises of improved playing time and wages of at least £70,000-a-week.
The youngster has seen an uptick in playing time in January, and though he remains without a Premier League start this season, he did receive a place in Maurizio Sarri's XI for the club's FA Cup clash against Sheffield Wednesday on Sunday.
Hudson-Odoi played the full 90 minutes in the 3-0 victory over the Championship side, netting his second goal of the season in all competitions with a 64th minute strike which put his side up 2-0 at the time.
Chelsea have denied Callum Hudson-Odoi's request for a transfer in the January window. He delivered it in person and wanted to move to Bayern Munich but he will have to wait until the summer at the earliest. Bayern's last official offer was £35m #CFC @goal— Nizaar Kinsella (@NizaarKinsella) January 28, 2019
His performances and talent have his team-mates hoping he commits long term, with Antonio Rudiger telling reporters Chelsea had to make sure Hudson-Odoi stayed.
The man himself has refused to be drawn into comment over his transfer situation, with Hudson-Odoi telling the BBC after his performance against Sheffield Wednesday: "I don't know. I can't say.
“I just keep working hard and you never know what happens. I can't say [if I spoke to Bayern].”
Hudson-Odoi is looking to continue in the footsteps of other English youth players who have ventured to Germany had found success.
Jadon Sancho, who has delivered six goals and nine assists in the Bundesliga this season with Borussia Dortmund, tops the list, but is not alone as Arsenal youngster Reiss Nelson, who is on loan at Hoffenheim, has scored six times this season in the German top-flight.