Terry thinks his England team-mate's new five-year deal at Old Trafford will make life difficult for the current Premier League champions.
He told The Sun: "I think Wayne staying will boost them and make it harder for us.
"On the back of what has happened United will probably go and spend in January and at the end of the season.
"The fact that clubs haven't been buying because of what's happened financially in the world has maybe helped Chelsea in the last few years. Wazza staying is massive for them."
Meanwhile, the 29-year-old has hailed Carlo Ancelotti's side for their defensive 'doggedness'.
The Blues have yet to concede a goal at Stamford Bridge and have only let in two goals from their opening nine league games this season.
He said: "The key to not conceding goals is having lads who are willing to run 50 or 60 yards to make a tackle to help their team-mates.
"We've always had that doggedness about us. One of the big strengths of this Chelsea team is that we don't concede a lot of goals and we don't drop too many silly points.
"There were times at the start of the season when we rolled teams over, scored five or six and looked really good.
"But we can also go to decent teams like (Aston) Villa, fight it out with them and come away with a good away point."