They want more entertainment from the team, a top five finish at least and ideally a British manager at the helm.
That comment about Allardyce's successor from Venky's chairman Anuradha Desai would appear to rule out the likes of Martin Jol, Sven-Goran Eriksson and Diego Maradona.
She told the Lancashire Telegraph: "We want good football and Blackburn to be fourth or fifth in the league or even better.
"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."
Source: PA
Source: PA