Redfearn replaced Evans at the New York Stadium earlier in the season, and since the two managers have taken a number of swipes at each other in the media.
Redfearn has criticised the quality of the squad he was left at Rotherham, but Evans claims that he was not fearing the drop when he was in charge of the Millers.
“I said I could have kept Rotherham up just turning up one day a week, I probably could have done it [turning up] just half a day a week,” Evans said.
“But my opportunity here is to bounce this team into the top half of the table, to try and push them towards them the play offs and to give the Leeds supporters a chance to dream.”
Rotherham are currently in 22nd position in the Championship table, and their form under Redfearn has not been particularly impressive.
The Millers did win their last match against Hull City though, which has moved them a lot closer to safety.
Leeds, meanwhile, have climbed the table since Evans took charge at Elland Road.
The 53-year-old boss was appointed after the side made a disappointing start to the campaign, but they are now only six points off the play offs and have won three of their last four matches.
Who's said what?
Redfearn says to the BBC that he has been left a squad of 'sub-standard' players at Rotherham.
Evans tells Sky Sports that Redfearn could be one game away from the sack.
Redfearn complains in the Yorkshire Evening Post that the players at Rotherham have told him that pre-season wasn't very good.