The three boys and coach were considered stateless even though they were born in Thailand. Many stateless people in Thailand come from areas where national borders have changed.
The museum, which is expected to take about five months and $300,000 to build, is being funded by a Thai artist.
The authorities have been concerned about the impact of sudden fame and media attention on the boys' mental health, so the news conference will be carefully controlled.
The 12 boys of the "Wild Boars" football team and their coach are recovering after last week's dramatic rescue and are to be discharged from hospital on Thursday.
"The 12 Wild Boars and coach have emerged from the cave and they are safe," the Thai navy SEAL unit said on its official Facebook page.
Officials have dismissed as speculation reports that the boys could be trapped for up to four months, although supplies have been prepared for that period of time.
Maing Hpone Sayadaw already revered by many in Myanmar, including some top leaders.