England under-21 coach Gareth Southgate has been made favourite by British bookmakers to take over from Hodgson, who resigned minutes after the 2-1 second round loss to Iceland, with Crystal Palace's Alan Pardew also at fairly short odds.
"I went to see the FA and said I wanted the job. They just looked at me and said, 'No, it's a lack of experience'," Shearer, whose managed Newcastle United for eight games in 2009, said on the BBC's 'Match of the Day'.
"I said, 'Well, you've hired experience, you pay them an absolute fortune, I could not have done any worse than those guys.'
"I would offer my services again, even if Gareth Southgate got the job, I would offer my experience of tournaments, for him to take players who have been there and done it has to be of benefit."
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(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
