Allardyce was fired on Monday, only 16 days after Venky's Group - the Asian poultry giant that purchased Blackburn last month - gave him a backing.
Blackburn's bosses want top-five finish and good play
Blackburn Rovers' new Indian owners intend to hire a British manager to replace Sam Allardyce and want the new man in charge to deliver entertaining football that can bring the club a top-five finish in the Premier League.
Allardyce was fired on Monday, only 16 days after Venky's Group - the Asian poultry giant that purchased Blackburn for £46 million (Dh266m) last month - gave him its backing. The team are in 13th place in the league.
Anuradha Desai, the chairman of Venky's, said the decision to sack Allardyce had been "a long time in our minds" and has a demanding set of targets for the former Bolton Wanderers and Newcastle United manager's successor.
"We want good football and Blackburn to be fourth or fifth in the league or even better," Desai told the Lancashire Telegraph.
"The fans should trust us because this is in the best interests of the club. Our thinking now is that it will be a British manager. But we are open if there is an outstanding candidate, someone who would be really, really good for the club."
Martin Jol, the Dutch coach who quit Ajax last week, was on Monday strongly linked with replacing Allardyce while the Daily Mirror even claimed Diego Maradona, the Argentina legend, was being lined up by Venky's.
Other potential candidates could include Martin O'Neill, the former Aston Villa manager, and two former Blackburn players, Alan Shearer and Chris Coleman.
Blackburn won the Premier League title in 1995, their first league crown for 81 years, but have largely been mediocre since and were relegated to the Championship twice.
In recent seasons, staving off relegation has been the priority rather than going for the title or even getting into Europe. Under Allardyce, who had limited funds available since taking charge in December 2008, Blackburn's style of football has been direct and physical but Desai is looking for a change of approach.
"It is nothing against Sam but we have a different vision looking forward and we want the club to grow," she said. "We had been talking to Sam in the past few weeks but he did not fit in with our vision for the club's future.
"We wanted good football, wanted the games to be interesting and, of course, wanted to win and to have good players.
"We needed to do some changes and Sam going is, of course, the main change. This is a major step but it was needed. We thought, 'Why delay?"'
The firing of Allardyce has been greeted largely with disbelief by players and managers alike.
Sir Alex Ferguson, the Manchester United manager and a close friend of Allardyce, said the decision "confounds common sense."
"I've never heard of such a stupid decision in all my life, it's absolutely ridiculous," said Ferguson, speaking on Monday after his team's 1-0 win over Arsenal.
"I don't know what they're doing up there, but deary me."