Shearer emerges as clear fans' favourite to take Blackburn job
The former Rovers striker came top of a newspaper poll as to who should be the new manager.
Local radio stations have also been inundated with calls championing Shearer's credentials.
But, on the day Hughes took over at Manchester City, Williams said: "If you are going to lose you manager this is the time to do it.
"There are still five weeks before the players return so we have some time to make the right appointment.
"We want to do it as quickly as possible but not this is not something you do with undue haste.
"We are an example to those who preach that in the Premier League there is nothing better for a club than stability, and that stability equals success.
"We have only changed manager once in eight years – four years of Graeme Souness followed by four years of Mark Hughes. That kind of stability has worked for us. Now we have to make the third one as good."
Shearer won a place in the supporters' hearts by helping the club win the Premier League title in 1995. He scored 130 goals in 171 appearances before joining his beloved Newcastle a year later for 15million.
In a poll conducted on the Blackburn-based Lancashire Telegraph website, Shearer was the fans' overwhelming favourite to succeed Hughes.
He got 46 per cent of the vote – nearly three times as much as his nearest challenger Paul Ince, the boss of MK Dons. Only 13per cent wanted the former Newcastle and Bolton manager Sam Allardyce, and just 3 per cent would welcome the appointment of Steve McClaren, who has been out of work since he was sacked by England last year. Shearer has admitted he wants to return to football one day, but has remained non-committal about when.