In their second match on 3 July, Greenland played the hosts and full FIFA members Iceland in Húsavík, losing 4–1, finishing third in the tournament.

The match drew international attention when China threatened to embargo Greenland's shrimp exports because of Tibet's contested sovereignty.

[10] About the issue, former DBU president Allan Hansen stated, "Concerning the GBU, I’m not convinced [they] officially applied for FIFA and UEFA membership at around the same time as Gibraltar.

As I’m informed, the GBU in the late nineties sent a letter [requesting clarification on a number of issues] but there were no follow-up actions."

[13] In 2011, Allan Hansen, chairman of the Danish Football Association stated that he did not believe that Greenland had the opportunity to become a member of FIFA or a confederation immediately.

One of the greatest barriers to admittance at that time was FIFA's strict regulations on stadiums and playing surfaces.

The most viable solutions would be to join UEFA or CONCACAF due to political links and geographical proximity, respectively.

[18] It was believed that UEFA would vote to change its membership requirements at the 41st Annual Congress held in Helsinki, Finland so that they were more in line with those of FIFA which allows non-independent states under certain conditions.

At that time, GBU chair John Thorsen expected that if UEFA changes its membership requirement, Greenland could have an application together by 2020.

[20] In May 2022 it was announced that Greenland had officially begun the process of becoming a member of CONCACAF and was expected to attend the body's next congress with observer status.

[21] Shortly thereafter it was revealed that the association and head coach Morten Rutkjær had begun to identify players in Denmark who have Greenlandic roots.

The association also appealed to UEFA for permission to play friendlies against San Marino and Gibraltar but were denied as it was outside of the FIFA match day window.

The Arktisk Stadion is a proposed new national stadium which would meet the requirements of international football confederations.

They played three matches in total, beating the national team of Gagauzia 2–0, drawing 1–1 with Zanzibar and losing 1–0 to Kyrgyzstan.