However, the report says that Sarri has "ruled out" the possibility of Loftus-Cheek being sent out on loan for the second half of the campaign even though his playing time in the Premier League has been limited.
There was little action on the pitch that would have warmed the cockles but the Blues did enough to progress through to the round of 32 after Olivier Giroud headed home early in the second half.
Sarri also confirmed that Alvaro Morata has remained back in London to train rather than play another match.
He brings things that no one else now does for West Ham, such as drive and aggression, as well as good technical ability.
Maurizio Sarri's side have been in superb form in Group L, winning all three of their matches so far, including beating this evening's opposition at Stamford Bridge 3-1.
It wasn't very easy to play a good game here, with the conditions.
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Both sides were the beneficiaries of comical own goals in a insane first half which ended with Glenn Middleton putting the Scots 3-2 ahead, but Luiz Adriano and Sofiane Hanni both scored in the space of 71 seconds to snatch Spartak victory.
He explained: "Today I was in trouble, too". 'I had fever. It was a very hard day for me'. "I don't know if I am improving or if it is only the temperature".
Salzburg, semi-finalists last season, qualified for the next round with a 5-2 thrashing of Rosenborg in the group's other match, with Japanese forward Takumi Minamino scoring a hat-trick.
Predicted Away XI: Arrizabalaga; Zappacosta, Christensen, Cahill, Emerson; Fabregas; Loftus-Cheek, Kovacic; Pedro, Giroud, Willian.
"It's true that I was hoping to score soon, because I came back late from the World Cup and after I lacked a bit of efficiency and luck sometimes", he said. "You always have to work hard and keep the faith". We didn't play very well. He is a very important for us.
"I think he's vital for the way Chelsea want to play. I think we could have done better". "It's very important because then we can talk again about this competition in February, when we will have another target".