The FA has named Hodgson as its top target after receiving permission from West Brom to talk to their manager about the vacancy created by Fabio Capello's departure in February. Its stance is a surprise given Tottenham boss Redknapp was the overwhelming favourite.
Mark Perryman said: "I think first of all, the FA needs to be open in terms of the situation. It's almost inconceivable they haven't approached Redknapp. I think the fans and the broader sporting public have a right to know what the situation is with Redknapp."
He added: "It's quite conceivable he has turned the job down but fans have the right to know.
"I am not saying Hodgson is the wrong man but clearly there was a popular mood around Redknapp and in the spirit of open governance, let's be clear what the situation was there."
Perryman was not convinced Redknapp was the right man for the job anyway.
He added: "The fans I know...there wasn't the degree of enthusiasm for Redknapp which was widely reported. There are enough fans who have been following the game for long enough to know he has won one trophy in 34 years.
"And also fans remember the last time we appointed the people's choice: Kevin Keegan. That was an unmitigated disaster.
"I don't think there will be a great wave of excitement about Hodgson but given that (Jose) Mourinho or (Pep) Guardiola are not likely to take the job...
"I don't think there is a great wave of enthusiasm about England in general at the moment - there are only 5,000 going to the European Championships which is one of the lowest travelling supports for a very long time."