Evans has been open about his desire to return to football after he was released from prison on Friday having served half of a five-year sentence for raping a 19-year-old woman at a hotel back in May 2011.
The former Wales international intends to clear his name, but amid reports that United are considering re-employing Evans, Webster told BBC Radio Five Live: "You will have young people cheering him on when he scores a goal. Not under my name, under my club or community."
Evans's sister Kylie hit back at the presenter by retweeting a message calling her a "hypocrite" after she posted a tweet a few weeks ago about meeting convicted rapist Mike Tyson.
She said: "Just bumped into Mike Tyson in the hotel lobby as I was randomly talking about him! I chickened out on asking for a photo...damn."
Webster later apologised for the tweet by saying: "In that split second I didn't register his past in my head. In hindsight, I'm not proud of that tweet, but that response has been another unfortunate example of berating someone for speaking out against rape."
Webster was sexually assaulted as a teenager.