The Blues were in control of the match but a number of missed chances meant they were always in danger of letting the game slip.
It is understood that the Hammers are preparing for the £5million-rated attacker to make the step up into the first-team and are expecting to hold talks over a fresh deal, despite him only signing a three-and-a-half year agreement last January.
And German star Rudiger has slammed his fellow defenders after another "gift" to throw the game.
However, according to Sky Sports News, he could set for a return to the bench as soon as next Monday when Stoke City visit the London Stadium.
Klopp says Salah is doubtful for Champions League tie against Man City
My team is extraordinary , it's not comparable to many others. "I bet Barcelona don't think they are through against [Roma]". City have now conceded six goals in their last two games following the 3-2 defeat to Manchester United on Saturday.
"I remember away at Manchester United, we were in control of the game and in the end we lost", Hazard added.
"I do think he is better than Adrian in goal. I play for my team, my family and my friends and anyone else who wants to comment, that's up to them and I don't care".
Everton have endured a hard season despite splashing the cash last summer, and will more than likely try to invest once again in the summer. But like the last few months we didn't and we concede.
West Ham boss David Moyes was full of praise for the 75-cap England worldwide after his display at Stamford Bridge, insisting Hart has given Gareth Southgate a timely reminder of his global credentials.