The TNT analyst was responding to James' recent Twitter post that read he was "taking mental notes of everyone taking shots at me this summer."
"I heard about LeBron's little tweet today that he's remembering everybody who said anything bad about him," Barkley said Thursday on ESPN Radio 103.3 Dallas/Fort Worth. "And he said 'everybody.' Well, I want him to make sure that he puts my name on that [list]."
Barkley took particular issue with the one-hour "The Decision" special on ESPN, where James announced he was going to sign with the Heat to play with friends and fellow superstars Dwyane Wade and Chris Bosh.
"I thought that his little one-hour special was a punk move," said Barkley, who earlier in the summer said James would never be Michael Jordan.
"I thought them dancing around on the stage was a punk move, and I thought he should've stayed in Cleveland. Him joining Dwyane Wade's team was very disappointing to me."
James has been the target of much criticism this summer and stated his plan for vengeance on Twitter.
"Don't think for one min that I haven't been taking mental notes of everyone taking shots at me this summer. And I mean everyone," James wrote.
Read more in The New York Post .