After 11 months out of football, Allardyce joined Blackburn in December 2008 after Paul Ince was sacked with the club lying second bottom of the Premier League.
Under Allardyce's guidance, Rovers finished 15th in 2009. Last season he steered them to the Carling Cup semi-finals in which they lost 7-4 on aggregate to Aston Villa.
Richard Bevan, the chief executive of the LMA, said: "When new owners take over a club, sadly, the manager's position often hangs by a thread.
"To Sam's great misfortune this has now happened twice and, on both occasions, it has been extremely difficult to understand the thinking behind the dismissal.
"It is ironic that one minute Sam can be proposed as the next England manager and the next, he finds himself out of work."
The club have not indicated when a new manager will be appointed.
Former Tottenham boss Martin Jol, who resigned as Ajax coach last week, ex-Aston Villa and Leicester City manager Martin O'Neill and former Rovers player Alan Shearer have been linked with the Ewood Park job.
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