The Mirror says Kyle Naughton and Vlad Chiriches are expected to depart White Hart Lane before the campaign starts, freeing up space should Richards arrive.
Richards, 26, played just two Premier League games for the Premier League champions last season.
And City have recruited Bacary Sagna on a free transfer to compete with Pablo Zabaleta for the right-back berth.
That means Richards will feature even less than during the last two campaigns.
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