The man, in his 50s, was quizzed by gardai after being picked up on Monday and detained at a Garda station in Co Monaghan.
He was released without charge yesterday afternoon and gardai said a file will now be prepared for the Director of Public Prosecutions.
Gardai also urged people with any information, “no matter how small or insignificant”, to contact Carrickmacross Garda Station on 042 9690197 or any Garda station.
The 21-year-old from Armagh was beaten to death by a gang of around a dozen men in a farm shed across the border near Castleblayney, Co Monaghan, in October 2007.
His family blames members of the IRA, but Sinn Féin has long denied republican involvement.
In July of last year, we revealed how Paul’s mother had a “positive meeting” with the Garda Commissioner and was hopeful for a breakthrough in the case 14 years after her son's brutal death.
In a statement Paul’s mother Breege Quinn wrote: “Today I met with Garda Commissioner Drew Harris to get an update on the investigation.
"It was a very positive meeting. He stated that the progress had been made following the Serious Case Review and that significant recommendations are being followed up.
"I’m hopeful that some of those recommendations lead to a breakthrough.
"I will continue to fight for justice for my son Paul.”
Paul’s family was given fresh hope at the beginning of last year as new DNA techniques are now being used to re-examine old exhibits in the investigation.
A dedicated scientist from Forensic Science Ireland had been working on the case, using the latest DNA technology.
Around 200 exhibits seized in Carrickmacross, Co Monaghan, were also being re-examined for traces of DNA.
These include clothing from some of the suspects and a vehicle.
Gardaí also said they planned to re-interview suspects and those who have made statements about the murder.
The PSNI was also set to examine items they have seized over the years.
The re-examination comes after a review by the Serious Crime Review Team was completed in late 2019.
In October of last year, gardai said that following a review of the case by the Serious Crime Review team, more than 300 new lines of inquiry were being followed.
A joint police operation in August of that year also saw gardaí and the PSNI visit a number of homes in the south Armagh area.
Garda Commissioner Drew Harris also visited the scene of the murder in August and met the investigating team.