The Football Association of Ireland's Board of Management held a meeting on Monday night to discuss the ongoing process of appointing a new manager.
And the board decided the best way forward is a "comprehensive assessment of the market" - to be undertaken by former Ireland midfielder Ray Houghton and the FAI's High Performance Director Ruud Dokter.
Houghton was partly responsible for the appointment of Trapattoni, the veteran Italian who secured qualification for Euro 2012 but was sacked this month following successive World Cup qualifying defeats to Sweden and Austria.
Ireland's chances of reaching Brazil are all-but dead, and the FAI sees no reason to rush into an appointment.
Martin O'Neill remains a strong favourite with the bookmakers, but any chance of a quick appointment now appears dead.
Instead King, who has worked with the likes of James McCarthy and Seamuis Coleman in his U21 role, is in line to lead the senior side into their final Group C games against Germany and Kazakhstan.
Harry McCue will assume King's U21 duties for October's European Championship double-header against Romania.