Mikel Arteta's side were targeting the Portuguese star despite already being close to sealing a deal for Martin Zubimendi, who last week completed a £60million transfer to the Emirates from Real Sociedad.
The Gunners' spending is nearing £200m this summer, with Christian Norgaard and Kepa Arrizabalaga also having completed moves, while Noni Madueke, Cristhian Mosquera and Viktor Gyokeres are set to sign in the coming days.
But their outlay could have been even higher after they made an approach for Palhinha.
The Gunners were looking for an experienced defensive midfielder and viewed Palhinha as a solid option because of his impressive showings in the Premier League during his two-year stint at Fulham.