Improved trade links and an inside track on the Western Sahara issue are among the benefits.
The North African country left the bloc in 1983 due to a row over Western Sahara.
Mohamed Abdelaziz died on Tuesday after more three decades of war and diplomatic struggle for the disputed territory with Morocco.
Ban Ki-moon sparked a row with Morocco by describing the disputed territory as under "occupation."
Morocco and Ban Ki-moon's dispute is the most serious since the 1991 ceasefire in Western Sahara.
Morocco has pulled its personnel from a U.N. mission in the disputed region.
Ban Ki-moon recently referred to Morocco's presence in Western Sahara as "occupation."
Ban Ki-moon has described the conflict as a "forgotten humanitarian tragedy."
Moroccan authorities have blocked the first Ikea store opening in the country.