King, 56, managed Ireland's women's side for a decade before being handed the U21 job in 2010.
Formerly a journeyman midfielder in Ireland's league system, King was involved in the national team coaching set-up during the 1990 World Cup, by which point he was a player-manager.
Former Ireland international Ray Houghton and Ruud Dokter - the FAI's newly-appointed high-performance director - have been tasked with finding a permanent boss for the Irish, whose 1-0 defeat to Austria two weeks ago all-but ended their hopes of reaching the World Cup in Brazil.
Trapattoni, one of the most respected coaches in world football, took Ireland to the Euro 2012 finals but saw his team lose every match in a tough group that included eventual finalists Spain and Italy.
- Sports & Recreation