Kyodo News of Japan cited Yusof, who is also Second Foreign Minister of Brunei, saying that he proposed the cease-fire until the end of this year in a videoconference with Myanmar's military-appointed foreign minister, Wunna Maung Lwin, on August 31.
According to the envoy, the military had accepted the proposal.
He said that this is a cease-fire to ensure safety and security of humanitarian workers as they go out and distribute aid to the people.
Yusof added that he has also passed his proposal indirectly to parties opposed to the military's rule.
Aid from ASEAN is being prepared as its member country Myanmar struggles with the triple crisis of political turmoil, a faltering economy and the COVID-19 pandemic.
The Indonesia-based ASEAN Coordinating Centre for Humanitarian Assistance is tasked with deploying humanitarian assistance to Myanmar, Yusof said.
The first batch of aid consists of medical equipment Myanmar urgently needs to help people who have become severely ill from COVID-19, such as oxygen compressors and protective gear, he said.
The next step is to procure COVID-19 vaccines for the country, the envoy noted.
Yusof was appointed as the special envoy in early August, months after ASEAN leaders agreed to a "five-point consensus" to help defuse the coup-sparked crisis in Myanmar.