The Cottagers had agreed a fee with Bayern in the region of €65 million ($70.5m) for Palhinha, but the deal was contingent on Fulham signing a suitable replacement before Friday night's transfer deadline.
The Palhinha transfer was made more complicated by the Bundesliga's window closing at 5 p.m. BST (12 p.m. ET), some six hours before it shuts in England. It means all parts of the transfer needed to be in place earlier for Bayern to complete the signing of Palhinha.
Despite the Portugal international flying to Munich to complete a medical, the deal was called off right before the closing of the Bundesliga window.
Sources have told ESPN that Fulham rejected an initial offer earlier this week but Bayern returned with an improved bid which was deemed acceptable, particularly as Palhinha was pushing for a move to the Bundesliga champions.
The 28-year-old only moved to Fulham from Sporting Lisbon last summer in a deal worth approximately £20m and excelled in the Premier League, scoring three times in 35 appearances last term.
He also netted a late equaliser as Fulham secured a 2-2 draw at Arsenal last weekend.
As Well as Hojbjerg, Fulham had also been tracking Monaco midfielder Youssouf Fofana as another possible alternative.
Meanwhile, Fulham are also closing in on the signing of Everton winger Alex Iwobi with the 27-year-old undergoing a medical on Friday morning ahead of a move worth around £20m.