Saturday's thumping defeat at home was their sixth loss at the London Stadium and second straight after losing 3-0 to Premier League new boys Brighton two weeks ago.
"I have to talk to the chairman because, of course, we have to discuss this defeat", he told BT Sport .
"And I am definitely not feeling a broken man". They have been supportive, very good to me in my two and half seasons, but the situation is very hard.
The 54-year-old Moyes is regarded by the club as the best immediate option to shore up West Ham despite taking Sunderland into the Championship last season, one that ended with him resigning from the club. "If he can play for Senegal, I think he should - good for rhythm", he concluded. This was not one of them, although the Hammers were just dreadfully flat, short of attacking spark or interplay between their attackers.
His presence was felt nearly instantly as Liverpool looked more threatening with him in the side, the speed he offers giving Klopp's attack an extra boost.
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Fellow star man Sadio Mane, however, could feature at some stage having returned to first-team training earlier this week after a spell on the sidelines nursing his injured hamstring. "I never did it before", Klopp said.
Mohammed Salah opened the scoring for Liverpool, as the away side hit their struggling opponents with a devastating counter attack. Sadio is not injured anymore, but is he 100% fit?
The heads were beginning to drop for Bilic's troops as Klopp's charges turned on the heat towards the final minutes of the first stanza, but could not add more goals to their two-goal cushion.
Yet the more direct approach got West Ham back into the game - for one full minute.
Huddersfield Town beat struggling West Bromwich Albion 1-0 at home to stay safely in mid-table - Dutchman Rajiv van La Parra deciding it with a curling shot just before halftime.