Winston Reid is a nursing a similar problem and will also be assessed.
Out-of-favour defender David Luiz remains sidelined with a knee injury.
"Chelsea have conceded just four goals in their last seven in all competitions". West Ham are second from bottom in the league, three points adrift of safety after losing nine of their 15 games so far.
"If they get sucked into an old fashioned derby scrap it could be a different story".
The goalkeeper is in his fifth season at West Ham and has been a regular between the sticks for much of that time, but has struggled for regular action in 2017.
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They have not gone nine top-flight games without a win since May 2011, a season which ended in relegation.
Moyes' final match as manager of previous Sunderland was a 5-1 defeat at Antonio Conte's Chelsea in May. However, if Moyes was able to somehow tempt him to the London Stadium, Evans would drastically improve the Hammers' defence.
Premier League strugglers Crystal Palace are reportedly fans of the keeper and could swoop if the player does not become content in East London.
This match will take place on Saturday, December 9.
Alvaro Morata has been involved in 13 goals for Chelsea within his first 14 Premier League appearances for the club.
Eden Hazard was in sparking form against Newcastle last weekend as the Belgium netted a brace.
Probability of away win: 67%.
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