"He is a player I knew when I was at Southampton and he was coming through the ranks," said Hughes.
"He was outstanding and has progressed year on year. I would be delighted to welcome him here.
"Wayne is already a successful player - he is an England international who plays for one of the top four clubs in the country."
City's oil-rich Arab billionaires Sheikh Mansour and club chairman Khaldoon Al Mubarak are set to bankroll a January spending spree with the intention of lifting City clear of the relegation zone.
Bridge has made 142 appearances for Chelsea in over five years, as well as earning 32 international caps for England.
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