Blackman, 28, is on the look-out for a new club in England following a stint with MLS side Los Angeles FC and is a free agent
Town are on the look-out for goalkeeping cover for first-choice Lee Nicholls, with Ryan Schofield sidelined until the spring with a shoulder injury sustained in the recent FA Cup win at Burnley, which saw Aussie teenage rookie Nicholas Bilokapic made his senior debut.
Reports suggest that Blackman could move to Huddersfield, who is said to be running the role over him in training.
Blackman made 28 appearances for the Millers last term during their unfortunate relegation from the second tier.
He made two starts for Leeds in the EFL in his time at Elland Road in the first half of 2018-19, having spent the previous campaign on loan at the Blades, making 33 appearances in all competitions.
Earlier in his career in 2014-15, Blackman temporarily linked up with Boro and made a famous appearance in an epic EFL Cup penalty shoot-out against Liverpool at Anfield, which saw the Teessiders edged out 14-13 on spot-kicks.