Chelsea thumped promoted Cardiff 4-1 for their fifth win of the season, keeping their 100 percent record and Sarri became only the fourth Premier League coach - after Carlo Ancelotti, Craig Shakespeare and Pep Guardiola - to win their first five games.
Terry turned down a lucrative one-year contract from Spartak Moscow this week after a late change of heart, but has been open in his desire to play on for one more season and has been linked with a return to Aston Villa.
The Premier League match between Chelsea and Cardiff will be broadcast live on CNBC.
Liverpool now top the table with four wins out of four, though Chelsea and Watford are also on 12 points after their ideal starts to the season. Still unbeaten, Manchester City beat Fulham 3-0 to remain two points behind the front-runners.
Watford had also taken 12 points out of 12, but Javi Gracia's Hornets lost for the first time this term by going down 2-1 at home to Manchester United. "If he wants to help us, I'm very, very happy". "I like that development", said Klopp. "We need to improve, but we are able to and can improve very quickly".
Sarri is still to taste anything but victory in English football, but had a scare early on at home to Cardiff when Sol Bamba put the visitors in front at Stamford Bridge.
Olivier Giroud laid on Hazard's first two goals, as the France target man continues to refine a potent partnership with his team-mate.
However, Cardiff's failure to significantly strengthen over the summer means they are liable to being outclassed at this level and were undone by the brilliance of Hazard.
Chelsea finally had breathing space when Willian was felled inside the area by Bamba and Hazard sent Etheridge the wrong way from the penalty spot.
"I think in this moment, we are very unsafe in the offensive phase but we are not so solid as I want in the defensive phase", Sarri said. "I can not change my mind after one match".
But Chelsea have learned fast enough to win and entertain so far.