Allardyce has been out of work since being sacked by Everton last summer and the 64-year-old has ties with the Terriers having played for them during the 1984-85 campaign.
But Hudson immediately began to run Allardyce close at the front of the market following Wagner’s exit.
David Moyes and Alan Pardew are other obvious early contenders with both out of work with Moyes having left West Ham United last May.
Pardew, meanwhile, parted company with West Brom last April.
Slavisa Jokanovic, Carlos Carvalhal, Chris Coleman, Daniel Farke and Gary Rowett were also among the early frontrunners.
Huddersfield announced the departure of manager Wagner by mutual consent at 6pm on Monday evening.
The Terriers sit bottom of the Premier League after Saturday’s goalless draw at Cardiff halted a club record nine straight defeats.
“David Wagner has departed his role as head coach of Huddersfield Town by mutual consent,” read a club statement.
“The 47-year-old leaves Town after detailed discussions with the board of directors, with both parties agreeing this is the correct move for the future of the club.”