Newcastle United had prioritised Højbjerg and were close to an agreement with Marseille, but the Denmark international ultimately turned down the move to St James' Park.
Aston Villa had stepped up their own pursuit of Palhinha in the meantime, working on a loan deal, but that approach broke down last week after Bayern made clear they would not sanction a temporary deal for the 31-year-old, with sporting director Max Eberl confirming there was no agreement to be found.
Bayern Munich remain insistent on a permanent sale, which complicates matters for Newcastle given the midfielder's contract situation and their preference for value in the market.
Palhinha is now reassessing his options, which include offers from Benfica and Sporting in his native Portugal, while manager Matthias Jaissle is understood to want an experienced organiser in midfield who can help guide his younger players following the departures of Sandro Tonali and Bruno Guimarães this summer.
Palhinha spent last season on loan at Tottenham, but Spurs chose not to make the move permanent at the end of the campaign, instead investing elsewhere in midfield.
Bayern paid close to £50m for the Portugal international when they signed him from Fulham in July 2024. Newcastle United remain separately in advanced talks over a different deal, working to sign right-back Amar Dedic from Benfica, as the club continues reshaping its squad following a summer of high-profile departures.
Arsenal had also previously registered interest in Palhinha, holding discussions before this summer's Club World Cup, though those talks appear to have cooled since Bayern's staff returned from their break.
With Newcastle needing experience in the middle of the park following the exits of two key midfielders, and Palhinha keen to re-establish himself in the Premier League after a difficult spell in Germany, both parties have reason to find a resolution before the window closes on September 1.