The club received around 40 serious applications, despite not advertising the position, and sifted through them to pick out their four favoured candidates at a board meeting on Wednesday.
Brian Laws remains favourite with the bookmakers, at 5-4 with Victor Chandler, although the Scunthorpe Telegraph have suggested he is not on the shortlist.
Another candidate favoured with the bookies is Alan Knill, a former Iron defender, who appears to have ruled himself out. Bury, where he is currently manager, issued a statement on Thursday saying he was "Going nowhere".
One name that appears likely to move up the odds is Mixu Paatelainen, the Kilmarnock boss. The Daily Express claimed on Friday that the Iron had approached the Scottish Premier League side for permission to talk to the Finn.