The Sunday World has app-ealed a High Court jury's award of €85,000 for defamation to former English Premier League star David Speedie.
The jury made the award last year after finding the paper had defamed him by saying gardai had reason to suspect him of being involved in criminal activity.
The Sunday World, in its arguments to the appeal court, said that question - of whether gardai suspected him - should never have been put to the jury.
Mr Speedie's lawyers argued that it was an appropriate question and opposed the appeal.
The paper wants the damages award overturned, while Mr Speedie wants the sum increased.
The case relates to two articles published in April 2011.
Mr Speedie (56), who played for Liverpool and Chelsea, among other clubs, claimed that Sunday Newspapers Ltd, publishers of the paper, defamed him by linking him to criminal figures in those articles.
The paper, its editor and the reporter denied the claim and said the words in the stories were true.
The first article was headlined "Kops and Robbers", while the second was published two weeks later in response to a letter from Mr Speedie's solicitor.
The second was headlined "Speedy the Snake", with a photograph of Mr Speedie handling a large snake.
Mr Speedie claimed the stories falsely meant he was engaged in criminal activity and had links to gangland crime.
Oisin Quinn, for Sunday Newspapers, said the High Court case had not been run on the basis of the question on which the jury decided to award damages - that the first of the two articles meant gardai suspected him of being involved in criminal activity.
It was not a reasonable finding that the first article had that meaning and the question should therefore not have been put on the issue paper the jury had to consider, he said.
This was the basis on which damages were assessed, making the verdict unsafe, Mr Quinn added.
Mark Harty, for Mr Speedie, said the meaning of the words was a matter for the jury and the way the case had been run was irrelevant.
The Court of Appeal reserved its decision.