They have seen him break into the first-team fold at Stamford Bridge this season, but feel more opportunities can be presented to him in Germany.
Chelsea, though, are understandably reluctant to part with a prized asset raised within their academy ranks.
They believe Hudson-Odoi’s ambition can be matched in west London, with Alonso among the team-mates of the hot prospect urging him to carefully weigh up his options.
The Spaniard said of an exciting club colleague: “He is a good player, but he is very young.
“He needs to have patience and to be hungry and fight for a place in this team.
“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.
“Bayern Munich? We are Chelsea, another great team and the Premier League is the most competitive league in the world.
“I don’t know why someone would go to Bayern Munich.”
Hudson-Odoi has only seen 42 minutes of Premier League football this season.
He has, however, recorded his first senior goal and an assist in Europa League competition.
His next opportunity to shine could come on Saturday as Sarri's men welcome Newcastle United to Stamford Bridge in the Premier League.
However, the offer of a fresh start in Munich and the option to inherit Bayern’s No. 10 shirt from former Chelsea star Arjen Robben remains on the table.