Bayern completed the signing of Sane from Manchester City in a deal worth €60 million ($97.4 million) on Friday, the Germany international putting pen to paper on a five-year contract.
When he is eligible to feature in 2020-2021, Sane will occupy the number worn by Coutinho during his season-long loan from Barcelona.
However, while advertising replica 'Sane 10' shirts for sale in their official club store, a Bayern statement read: "Out of respect for Philippe Coutinho, who is the current number 10 and could play in the upcoming DFB-Pokal final in Berlin and any games in the [UEFA] Champions League in August, Sane decided not to use the number in his photos."
The decision appears to suggest Coutinho is unlikely to remain at Bayern for the long term.
The Brazil international has been linked with a host of clubs across Europe after the Bundesliga champion let its option to sign him permanently expire.
Bayern chairman Karl-Heinz Rummenigge has not ruled out moving again for Coutinho entirely, saying: "We'll see if he still has a role to play with us or not."