Parker puts his belt on the line in Manchester on September 23 and is now into the second week of sparring.
Barry has him working with some classy talent with his current training opponents being world title contender Malik Scott and fellow American Xavier Vigney whose 2.03m frame replicates the lanky Fury.
Parker said he was getting in some "great rounds" with the pair as his Las Vegas training camp intensifies.
The 36-year-old Scott has 38 wins, three losses and a draw in a professional career dating back to 2000.
