After Chris Sutton's departure for Birmingham last week, The Sun reported that Hartson will follow to England, to be closer to his wife and children.
However, Barnett denied there are any problems with his client, Celtic's top goalscorer this season.
He said, "I will be amazed if ever the press tells the truth.
"They should just all concentrate on writing children's books because they know nothing.
"He has two years left on his contract after signing a new deal and he is fine at Celtic.
"All I can tell you is people make up their own stories instead of trying to find out the truth."
Good stuff.