The former England international is a free agent following his release from City at the end of last season.
He spent the majority of the year with Brighton on a loan basis and having been impressed with his performances, Redknapp is keen to recruit the 32-year-old in time for the new campaign.
"I'm trying to get Wayne Bridge in. I thought he did fantastic at Brighton last year and he would be a good left-back for us," the veteran boss told Sky Sports News. "He's got got great experience and looks in good shape. He's a player that I really want to bring in on a free. We are pushing for that one."
Bridge joined Man City in 2009 following a six-year stint with Chelsea.