Former Man City boss Manuel Pellegrini is the latest man to be linked with the Everton job.
Premier League rules allow points to be deducted retrospectively.
West Ham have appointed David Moyes as first-team manager on an 18-month contract.
"It is with great disappointment that we've had to make this decision."
"Away we are not doing bad, but our home games having just one point from 18 makes it so difficult."
Manuel Pellegrini is aware his need to improve their home form and hopes that will start on Saturday.
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"Roberto didn't have good performances when he played but I always say he has a career behind him."
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Manuel Pellegrini has admitted West Ham's form is not good enough as they travel to Southampton.
Pellegrini insists West Ham will stick to their beliefs as they look to build on Chelsea win.
Manuel Pellegrini was pleased that West Ham stuck to their philosophy to help them beat Chelsea.
Pellegrini also admitted his goalkeeper is 'not in a comfortable position'.
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"I think he only took charge yesterday, so probably we will see Tottenham playing in a similar way."
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Pellegrini is happy with the start to the season but picked out two areas the Hammers must improve on.
Manuel Pellegrini hopes the EFL Cup defeat to Oxford was an "accident" ahead of Bournemouth clash.
But the West Ham boss also blames the players who were somehow battered 4-0 by Oxford.
"We must demonstrate that we are able to play exactly the same way they do."
Pellegrini believes Wilshere has put his injury problems behind him as he battles for a regular place in the West Ham line-up.