Terry told the club's official website, www.chelseafc.com: "Obviously, I have great memories of Stamford Bridge.
"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.
"We're talking about the next generation of kids beyond that as well. It excites me because I know for sure that we can grow."
He added: "For us to go further, we might need to move, and we have to trust our owner (Roman Abramovich).
"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.
"We have to remember that London is a hotspot, west London especially, and big development companies can build substantial flats and penthouses here, and if we're not putting our name in the hat for these sites, then without a doubt they'll be snapped up by developers."
Several supporters' groups have united to try to convince shareholders of Chelsea Pitch Owners (CPO) - who have been in possession of the land beneath Stamford Bridge since the 1990s - to vote against the club's proposal.
Terry is the CPO president.
The 'Say No CPO' campaign plan to distribute 10,000 leaflets before this weekend's Premier League match against Everton.
Source: AFP
Source: AFP