Hughes initially began his own managerial career at Falkirk in a joint role with Owen Coyle, who went on to success on his own with St Johnstone and Burnley.
Falkirk's board were meeting on Tuesday evening to consider drawing up a shortlist for the job.
Partick Thistle's Ian McCall was one of those thought to be up for discussion, but it appears that he is out of the running having gone on to sign a new contract with the First Division club on Wednesday.
Former Celtic and Wales striker John Hartson is thought to be interested in being Falkirk manager.
Alex Rae, the former Dundee manager, former Scotland defender Steven Pressley, who retired as a player with Falkirk at the end of the season, Queen of the South manager Gordon Chisholm and Falkirk youth coach Eddie May are also thought to be in the running.
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