The Manchester Evening News says Rodgers has hinted he could be ready to make a move for City full-back Richards.
He has hinted he is looking for someone with Premier League and Champions League experience, of which Richards has both.
BR said: “We’re in a position now where we’re going straight into the group stage of the Champions League and we’re going into the Premier League next season with an expectation and a belief that we can win the league.
“We need players that have those qualities.”
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