The Portuguese midfielder had agreed personal terms with The Bavarians and completed his medical on deadline day, but Fulham blocked the move, having failed to sign a suitable replacement in time.
The Cottagers were linked with moves for Scott McTominay and Pierre-Emile Hojbjerg on September 1, but were unable to land either signature, though they may still consider going back in for those players in January.
According to a report from the Evening Standard, with the departure of Ryan Gravenberch to Liverpool, Bayern feel they are now short of a midfielder and plan to renew their interest in Palhinha during the next transfer window.
Fulham boss Marco Silva has said that he does not want to lose the 28-year-old who arrived just last summer, but the club seems to be willing to let the player leave for the right price and if they can secure a worthy replacement.
Bayern had a disappointing transfer deadline day as they were unable to secure signings beyond Fulham's Palhinha, missing out on players like Chelsea's Trevoh Chalobah and Southampton's Armel Bella-Kotchap as well.
For now, a January transfer to Bayern Munich remains a possibility, and it would offer the 28-year-old midfielder an upgrade after his one season with Fulham unless there is a change of heart by the Bundesliga champions.
Palhinha made 33 appearances for the Cottagers in the 2022-23 Premier League season and scored three goals, helping Fulham to a top-half finish.