"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.
Sometimes getting back playing quickly is the best thing to do."
Moyes says Evra's leadership qualities made him an attractive proposition to the club but maintains he wants the defender to primarily concentrate on matters on the pitch.
He said: "We like his other qualities but we got him here to play. Hopefully we can get him ready as quick as possible.
"I know Pat well and I know what he is capable of. I know his leadership qualities and what he will bring to the dressing room. Also his level of professionalism is as good as anybody.
"He's seen and worked with the best so hopefully he can pass that on to the players.
"We needed him after Arthur [Masuaku]'s suspension. If Aaron Cresswell got injured we would be left short.
"We were so busy with other players we didn't do it in January. When the window closed and it was a bit calm we could get it done."