Evra signed for the Hammers on Wednesday having been released from his contract with Marseille in November, following an altercation with a fan before a Europa League match. He is not eligible to play in any UEFA competitions but is clear to play in the Premier League.
When questioned Moyes said: "There's a chance. He's not too far away, he has been training."
"He played in November for Marseille so he's no different from someone who may have had a long 10 or 12-week injury," added the Scot. "Sometimes getting back playing quickly is the best thing to do."
West Ham are hoping that Evra can impart some of his wisdom and experience to the rest of the team, but his priorities will be his own performances on the pitch. "We like his other qualities but we got him here to play. Hopefully we can get him ready as quick as possible," Moyes continued.
Evra won five premier league titles with Manchester United and previously worked with Moyes when he managed the 'Red Devils' for a season.