The Millers are desperate for reinforcements and will now take a look at Best after last week Redfearn said there was little chance of anything happening.
He is without a club since his summer release from Blackburn and has also been training at Huddersfield lately.
Redfearn has been impressed with the 29-year-old and thinks he could be an answer to the Millers' striking woes.
Redfearn said: "He has come down to train with us, he is without a club, a free agent.
"He looks strong, he looks like he has looked after himself, he trained this morning and looked really sharp.
"He is a player that carries good pedigree, he knows his strengths, he has played at the level above, he is a scorer so if we can get him where we need to get him it's an option.
"With Leon, he's a bit more established, you know what you're getting and we can get him up to speed quickly. He looks the part."
Drury is also without a club, but is not eligible to be signed until January following his exit from Bristol Rovers after just a month.
The 22-year-old was released by Manchester City in the summer and can play right-back or right wing.
"Adam is a young boy that is in between clubs," Redfearn added. "He has got good pedigree having come through at Manchester City, he can play one or two positions, he is comfortable with the ball.
"It's an opportunity to have a look at him. We are just having a look at him, we've not got to the next bit yet."
