The former Manchester United (aged 24) trainee has made over 70 appearances for Rovers but lost his place this season.
A Blades spokesman confirmed: "we're talking to him about a possible deal. There's no truth in the stories that a deal has been agreed, but we are hoping to sign him."
United fans should remember Curtis, while at Old Trafford he moved to Barnsley on loan. He played in the South Yorkshire in March 2000 at Bramall Lane where the Reds where in front 3-2 with just seconds to spare.
In a act of desperation, Simon Tracey hammered the ball down the field where Laurent D'Jaffo heading on but there was no one around to follow up. The ball fell to Curtis who tried to head back to Kevin Miller but before he could get it Marcus Bent chased in and chipped the ball over Miller and into the back of the net.