The centre-back, who has been capped 81 times by his country, has been in fine form for the Premier League leaders in recent weeks with many believing he had warranted a return to the international fold, where he has not featured since June 2011.
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"I'm not going to talk about Rio, I don't want to talk about him,” Hodgson told reporters. "People can write what they want to write. I can't be fairer than I've been.
"It seems to me that every other day I have to answer questions about Rio. I'm not prepared, every time we play a game, to keep revisiting something I've visited every single press conference for the last 10 months.
"For years and years, England had a centre-back pairing [Ferdinand and John Terry] everyone was really satisfied with, two very good players.
"For various reasons, we've moved on from that and so we have to try to solve the problem.
"I was pleased with Chris Smalling and Gary Cahill [against Brazil on Wednesday] and before that Phil Jagielka and Joleon Lescott have done a good job for us as well. It's not as if we haven't got any defenders.
"Smalling can bring the ball out. He played on the left side against Brazil but if you play him on the right he's not lacking ability on the ball and neither is Gary.
"It's being unfair to the two of them to suggest they can't do that. We're not talking lower league. We're talking international football, England against Brazil - whoever you would play at centre-back would have problems against that quality of opposition."