The 48-year-old took charge at Stamford Bridge in the summer of 2016. In his debut season in England, the former Juventus and Italy coach helped the Blues win the title comfortably. Conte also saw his side suffer a defeat at the hands of Arsenal in the FA Cup final last campaign.
Chelsea have struggled in this calendar year in all competitions. A poor run in the league in January coupled with elimination from the Carabao Cup semi-final has raised questions over his future at the club beyond this season.
Two back-to-back defeats at the hands of Watford and AFC Bournemouth in the first week of February resulted in uncertainty around Conte's future at the club, despite the manager reiterating his desire to see through his contract. However, the Italian has helped his side bounce back with a 3-0 victory over West Bromwich Albion.
Chelsea are fourth in the table with 53 points after 27 games, trailing league leaders Manchester City by 19 points. Carragher claims a top-four finish and lifting the FA Cup or the Champions League will be a successful season for the English champions.
"There's no doubt for me. Conte has done a superb job. His points total since he came to England is only bettered by Pep Guardiola and that says a lot about him as a manager," Carragher told Sky Sports.
"Last season Chelsea blew everyone away. To be so far ahead, not only of the best clubs in the country, but some of the best managers in world football showed what a top manager Conte is.
"It remains to be seen whether you class this season as a success or not. If they can finish in the top four and lift a trophy, that is success, considering how competitive the top six teams are in the Premier League.
"Even if Chelsea only finish in the top four, that's still been a great two years, in which he's taken them from 10th - which admittedly was a false position - won the title and given them Champions League football before he goes."