Chelsea are yet to open talks with Fabregas over an extension to his current contract, which expires next summer, and his future at Stamford Bridge looks more precarious with Jorginho established as Sarri's preferred midfield playmaker.
And under Maurizio Sarri, the Blues have grown in leaps and bounds and a number of fans are putting money on them to pick up the trophy at the end of the season.
"The character we showed at the back end of past year is still very much within the team, and it will sustain us and make sure that we're successful".
'In football being a teacher's pet doesn't really come into it", he says, "and there's a lot about our relationship that people don't know so pet does not come into it'.
"We'll always ask questions of good oppositions because we are a good team".
And Alvaro Morata capped the win with his second goal in as many games when he lifted the ball over keeper Alex McCarthy after being set up by Hazard in injury time.
Last season Loftus-Cheek enjoyed an impressive loan spell at Crystal Palace and was rewarded with a place in England's World Cup squad.
He confirmed there had been no talks about a new Blues deal, adding: "I have eight months left and at the moment I'm gone". A lot of these guys have played together for a long time so they have an understanding of each other as individuals, team-mates and persons, and that's important.
Chelsea fans need to start seeing more from Giroud - who earns £120,000-a-week, according to spotrac.com - and Southampton could be the flawless opponent for him to rediscover his goalscoring touch.
Redmond would have pulled a goal back but for a fine save by Kepa, who pushed his shot on to the bar and also kept out a late strike from Ings. (It is) very hard in the Premier League to stop a team having any chances - it's very, very rare. "So I think this case, for that kind of player, it's better to play for 35, 40 minutes than to have training".