The 32-year-old joined the Championship club on a season-long loan deal this summer and is enjoying himself at the Falmer Stadium.
"You never know," Bridge told The Argus. "Obviously, I want to do well for the club and if the opportunity [to stay here permanently comes up, it might suit me.
"I have enjoyed every minute here, so I definitely wouldn't say no to that. Everyone that knows me, friends and family, have seen the change in me.
"Over the last few years, it has been difficult but they seem to think that I look like I like football more, so it can't be a bad thing."
Bridge has been on the books of City since 2009 but has played on loan at West Ham United and Sunderland since then.