The playmaker has been out of the national set-up since 2014, largely due to injury troubles.
Having regained full fitness ahead of the Africa Cup of Nations early this year, the 28-year-old surprisingly turned down a call-up, opting to focus on his club career.
“I don’t understand why the boy [Asamoah] has refused to come play for the nation, maybe there is something we don’t know," Akonnor told Happy FM.
"He was one of the key players when he played for Ghana, and we always looked up to him to deliver and he delivered all the time.
“He is not the only one [needed in the team]; I think we have a lot of talent who play in Europe.
"We are spoilt for choice but when we start to have the situation where players are refusing to come, it becomes an issue for us.
“I think the authorities or the manager himself should sit with the players and talk to them so they come help the Black Stars because we need their quality."
Asamoah has represented Ghana at six tournaments comprising four Afcon events and two World Cup gatherings.
He last featured for the Black Stars in a 2015 Afcon qualifier against Uganda in September 2014.