Puel spoke to the media ahead of a game against Liverpool on Friday, and the topic of Simpson's injury was discussed.
He said: "I spoke about it being a few weeks [on Tuesday].
"I don't know; maybe four or five weeks. We'll see when he can come back into training."
Simpson was unable to stay on the field during the 2-2 draw with Manchester United, coming off in the 57th minute due to a hamstring injury. The injury will now keep him out for at least a month.