Mr Hamilton, who has been the PSNI’s chief constable since 2014, is set to retire.
Four candidates are to be interviewed today, the BBC report.
Two candidates from within the PSNI — Mr Hamilton’s current deputy Stephen Martin and assistant chief constable Mark Hamilton — are to be interviewed alongside two external candidates.
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The external candidates are Jon Boucher, the outgoing chief of Bedfordshire Police who is currently leading the ‘Operation Kenova’ investigation into the activities of the alleged agent within the IRA referred to as Stakeknife, and Simon Byrne who is a former chief of Cheshire Police.
The new police chief will take up the position next month, when Mr Hamilton is due to step down.
The BBC say the selection process will take place over two days selection process will take place over two days with a special meeting of the board set for 5pm on Friday.
Independent recruitment specialists have been hired to oversee the appointment.
A senior occupational psychologist will “dip sample” notes taken by selection panel members and ask them to justify the marks they allocate to shortlisted candidates for the chief constable’s job.
A preference for applicants to have served outside Northern Ireland has also been dropped from the list of desirable criteria in the selection process.
Those steps are among several beefed-up scrutiny measures introduced following controversial comments by Sinn Fein leader Mary Lou McDonald on who should succeed the retiring George Hamilton.
Mrs McDonald was accused of undermining the integrity of the recruitment exercise when she said she did not have confidence in any prospective candidate from within the PSNI.
Her remarks in February prompted calls for the customary Sinn Fein representative to be excluded from the selection panel assembled by the PSNI’s oversight body, the NI Policing Board.
Those calls were ultimately resisted, with board members instead agreeing to introduce new quality assurance measures to safeguard the process.
Details of the steps emerged as the recruitment exercise for the £207,500-a-year job went live in April.