Owner Roman Abramovich is hoping to buy out the Chelsea Pitch Owners (CPO) stake in the Bridge's freehold, which is seen as a significant step in departing their current location.
However, Terry, who is the current president of CPO, believes that a new stadium would benefit the club.
"Obviously, I have great memories of Stamford Bridge," he told the club's official website. "But what excites me is the thought of my kids, who are Chelsea through and through, being able to grow up watching the team play in a big stadium.
"It's not hidden that other clubs throughout Europe have gone out and bought sites for big stadiums.
"For us to go further, we might need to move, and we have to trust our owner. He has been amazing since he bought the club, along with our fans as well. No one is saying it is going to be an immediate change but we need to be looking."
The Blues entertain Everton in the Premier League on Saturday.