Barry George's supporters say he is unlikely to succeed in any attempt to overturn his conviction for murdering Jill Dando.
George, who is starting a life sentence in prison, is said to be devastated by the verdict, which his supporters claim bears all the hallmarks of a miscarriage of justice.
But John McManus, from the Miscarriages of Justice campaign and support group, said George was very unlikely to lodge a successful appeal.
"It is a Catch 22 situation for him," he said. "He has been convicted on circumstantial evidence but the Court of Appeal will not look at anything based on circumstantial evidence.
"From what I can see it looks very unlikely that he will appeal. He needs fresh evidence, but it's going to be very difficult to find fresh evidence.
"This case has the hallmarks of a miscarriage of justice. He doesn't seek attention so if he killed her to become famous why hasn't he confessed? He doesn't fit the profile."
Mr McManus said it was unlikely George would be given permission for a hearing at the Court of Appeal.
His only option would then be to apply to the Criminal Cases Review Commission, which could take several years to reach a decision, he said.