Sane scored Germany's final goal in Tuesday's 8-0 Euro 2020 qualifying demolition of Estonia in Mainz, impressing throughout in attack.
The winger had an indifferent season at club level with Premier League champion City, scoring a respectable 10 goals, but only starting 21 matches, six fewer than the 2017-18 campaign.
Sane subsequently emerged as a primary target for Bayern, whose rebuild job will continue in the close-season after the departures of long-serving duo Franck Ribery and Arjen Robben.
Bayern have rued City's "insane" valuation of the winger, though Sane failed to commit to Pep Guardiola's side post-match.
When asked about the Bayern speculation, Sane said: "I'm going on holiday now. Everything else will be seen.
"That's it with the questions about Bayern Munich."
Sane, 23, has been at City since 2016, when it reportedly paid Bundesliga outfit Schalke an initial £37million.