Terry left Chelsea last June after 22 years and 15 major trophies.
He is still the last Chelsea academy product to play regularly in the first team – and many managers have tried and failed to find the next one.
Conte believes 21-year-old defender Christensen can thrive for the Blues for some time to come.
“This is a big comparison — John Terry wrote the history of this club and won a lot,” Conte said.
“I wish Christensen to have the same career as John. I think he has the right characteristics to play for this club for many years, to become an important player for this team, for this club.
“Christensen is maybe the best surprise from the start of this season, despite his young age.
“He’s been the best surprise for me, for the club, for his team-mates, for the fans.”
It is not a total surprise. The Denmark international thrived in two years on loan in the Bundesliga with Borussia Monchengladbach and has been promoted as the benchmark for Chelsea’s young players.
Conte says he will play his more peripheral players in tonight’s Carabao Cup quarter-final with Bournemouth.
And that might mean a rest for Christensen, who has displaced David Luiz as Conte’s first choice in the centre of his three-man defence.
Conte would not be drawn on whether Christensen merits a new contract, saying it was a club decision, but praised the defender who signed from Brondby as a 16-year-old in the summer of 2012.
Christensen was thrust into the starting XI when Luiz was dropped for the Premier League clash with Manchester United on November 5 and has retained his place since.
“Every time I decided to give him the opportunity to play, he played with an amazing performance,” Conte added.
“These performances convinced me that Christensen has to play with regularity.”
Christensen has seized his chance. Michy Batshuayi has not, but the striker is to get another opportunity against Bournemouth.
Danny Drinkwater and teenagers Ethan Ampadu, Callum Hudson-Odoi and Dujon Sterling are also expected to be included, but Charly Musonda (groin) has joined Luiz (knee) in the treatment room.
Conte suggested Belgium striker Batshuayi’s £33m price tag — the fee when the Blues signed him from Marseille in July 2016 – was due to his position.
“When you are a striker in this crazy market, your valuation is very high — only because you are a striker,” Conte said.
Conte says he is happy with this season’s contribution from Batshuayi, who scored the decisive goal in the 2016-17 title race which delivered the Premier League in Conte’s first season at Chelsea.
That was on the 24-year-old’s 18th Premier League substitute appearance without a start.
And Batshuayi has been regularly overlooked to start this term, even when Alvaro Morata has been injured, with Conte preferring to deploy Eden Hazard as a ‘false’ nine.
“This season, if you consider his (ankle) injury for a month, he had his chance,” Conte added.
“(To play more) he has to show me that he’s better than Morata, or than Hazard. It’s very simple.”
For his part, Bournemouth manager Eddie Howe has warned he will not rush into the transfer market next month despite his side’s precarious position in the Premier League.
The Cherries have slipped to 16th in the table, just one point above the relegation zone, following a six-match winless streak.
Howe’s side were dealt a crushing 4-0 home defeat by Liverpool last weekend, but the Bournemouth boss is confident his squad can provide a swift turnaround in fortunes without the need for reinforcements in January.
“At the moment we are not looking at anything in January,” Howe said. “If we can keep the squad together, and pick up results than everything changes.
“In January, it is a very difficult window to make too many changes in terms of incomings. It is an incredibly expensive market with not too many players to choose from. Ideally we would not be doing too much in that market.
“Of course, injuries force your hand to a degree, but we are hopeful injuries suffered by the players are not serious. We need to be adaptable so it is not impossible.”