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If ever the people in charge decided I was the man they wanted then I would be delighted
The Tottenham boss also said he did not hold any grudges at being overlooked.
Redknapp had been the favourite to succeed Fabio Capello since the Italian quit in February.
"No problem," Redknapp said. "I wish him [Hodgson] all the best. He's a great guy. I've got a great job here (at Spurs). I don't hold grudges."
The Tottenham manager spoke to BBC Sport at Spurs' training ground on Monday morning after the FA made its approach to Hodgson on Sunday. The West Brom boss is due to be holding talks over the role, and is expected to be appointed in the next 48 hours.
Redknapp added: "I'm very happy to be doing what I am at Tottenham.
"I suppose it's all dragged on a bit [selection process] but it's no problem and I'll just get on with my job here and we are looking for a good end to the season.
"I like Roy, he's a top man and a good guy and I wish him great success.
"England have some fantastic players and I'm looking forward to the Euros. Life couldn't be better: the sun is shining, I'm in good health and I'm a very lucky man."
Redknapp had received widespread backing in football since Capello's departure and the approach to Hodgson surprised many.
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In February Hodgson himself said: "Harry's receiving all the backing from virtually all quarters, but it's up to them to decide what they want to do and I don't think it's right for people like myself to say: 'I'm interested or I'm not interested' in the job because I've no idea what the FA have got in mind and what they want to do.
"I think it's right to keep one's options open," he added.
Redknapp had described the England job as the "ultimate job for an Englishman".
"You have to look at the whole thing and realise just what a tough job it is," he said in February.
"No-one has a magic wand. They've all found it very difficult. Whoever takes that job has a real job on his hands.
"At my age (65) I have to do what's right for me. Whatever decision, my family will come first now. If the opportunity comes I will look at it in then."
Harry Redknapp has wished Roy Hodgson well after the Football Association approached the West Brom manager for the England role.