Hodgson's Reds were beaten 2-1 by Spurs at White Hart Lane on Sunday thanks to a last-gasp goal from Aaron Lennon and the losing manager was confident his counterpart would be a great fit to succeed Fabio Capello.
"Harry's got the attributes to do the job, no doubt about it," Hodgson said.
"We'll have to wait and see but it would surprise me if the FA don't choose at Englishman to take over from Fabio should he indeed decide to step down after the European Championship in 2012.
"Public opinion seems to favour an Englishman being in charge again and Harry will be a major candidate because of what he's achieved.
"It doesn't surprise me that Harry has said he wants it because it's the pinnacle of everyone's ambition."