The Peruvian, who usurped Julio Leal in March, has helped steer Pirates within touching distance of retaining PSL honours.
Bucs, the MTN8 and Telkom knockout champions, are two points clear of Soweto rivals Moroka Swallows at the summit with two games left against Bloemfontein Celtic (at home on Saturday) and Golden Arrows (away).
And Josephs feels it is a no-brainer that Palacios must stay.
"Of course he (Palacios) should stay," Josephs said.
"If you could see our training sessions now, I can tell you, it has been a while since we enjoyed them.
"He has made us comfortable. He has put in an effort with the team."
Palacios was formerly the club's head of youth.