The rumours emerged despite Bayern having already wrapped up their key summer transfer business early, a strategy that pleased honorary president Uli Hoeness, though various links persisted around the club right up to deadline day and beyond.
Cherki, who has regularly started for Manchester City this season without yet completing a full 90 minutes, had been touted as a potential target for the German champions.
According to Bayern insider Christian Falk on his website, cfbayerninsider.com, there is currently nothing to the reports.
"I asked Max Eberl about this and he made it clear that there are no plans to sign Cherki in the winter transfer window," Falk said.
"Bayern don't tend to make big transfers like Cherki anyway, who would be very expensive in January, unless something catastrophic like a serious injury happens."
Bayern's interest earlier in the year had in fact centred on a different attacking option entirely, before the club turned instead to Ismael Saibari. The Morocco international joined for a €50 million fee from PSV Eindhoven, having emerged as Bayern's preferred alternative once Anthony Gordon's valuation made him unaffordable following interest from Barcelona.
The wide attacking positions are currently occupied by Saibari, but that picture could change next summer depending on developments elsewhere in the squad. Michael Olise's situation is being closely watched, with his contract situation unresolved despite Bayern's desire for him to extend his stay in Munich.
"Bayern do want Michael Olise to stay, but as long as the French winger doesn't sign a new contract, his future remains uncertain," Falk said. "Luis Diaz has so far struggled to match last season's form, and that could become a problem for the club if his form doesn't improve.
"Serge Gnabry could also need replacing. Taking all factors into account, there could be room for new arrivals in attack."
Any fresh move for Cherki, then, appears to be a matter for next summer at the earliest rather than the upcoming winter window, with Bayern's focus for now firmly on the squad they have already assembled.