The envoy, Christopher Ross, is also to return to Western Sahara which Morocco took over in 1975 following a Spanish withdrawal, a UN spokeswoman said.
Morocco's claim to the territory is not recognized internationally and a UN decolonization committee is discussing the case as Ross embarks on the tour. A Polisario Front separatist envoy called for greater UN "determination" over the prolonged dispute Thursday.
Ross, who Morocco last year demanded be replaced, is expected in Rabat this weekend, diplomats said.
"During his trip, he will hold bilateral consultations with the parties, Morocco and the Frente Polisario, and with the neighbouring States, Algeria and Mauritania," UN spokeswoman Vannina Maestracci told AFP.
"He also intends to visit Western Sahara," she added without giving details of the timetable.
Ross, who will report back to the Security Council on October 30, discussed Western Sahara with UN officials and Tunisia's foreign minister in Tunis this week, the spokeswoman said.
Morocco battled Algerian-backed Polisario Front rebels in the phosphate-rich territory until the UN brokered a ceasefire in 1991. The Polisario wants an independent state and UN resolutions have called for a self-determination referendum.
But efforts since then to organize a vote have been blocked amid. Morocco has agreed only to give Western Sahara greater autonomy, while it has faced accusations of rights abuses in the territory.
Ross's efforts to bring the two sides into talks have faltered amid some acrimony. The Moroccan government last year briefly demanded that UN leader Ban Ki-moon replace the envoy.
"I fear that Ambassador Ross will again come back empty-handed because Morocco is unwilling to cooperate with an open and transparent decolonisation process," Polisario Front envoy," Ahmad Boukhari told a UN decolonization committee on Thursday.
He called on the UN leadership to handle the case with greater "determination".
Morocco is to address the committee on Friday and is expected to again put its case that independence for Western Sahara is unworkable.