It is understood that Dunne was advised to raise the price he was charging for cocaine, because he was undercutting the rest of the dealers in Dublin, who are Kinahan's other clients.
Dunne (34), who reportedly had become increasingly erratic because of his own cocaine abuse, refused to do so.
According to security sources, Kinahan told associates that Dunne was also a serious liability due to the number of murders he had ordered.
A source said: "When Kinahan speaks, you listen, that's the unwritten rule. But Dunne was too pig-headed and insisted that no one was going to tell him what to charge for his product."
Kinahan organises major shipments of drugs from Russian, Turkish and North African cartels into Ireland, fuelling the country's gangland activity.
A 'dapper don', he has a reputation for being well dressed and well educated, speaking three languages.
The criminal is currently incarcerated in Belgium for money laundering.
It is understood that Kinahan sanctioned the murder which was carried out by a gang of ruthless young thugs.
The gang, which is heavily involved in armed robberies and drugs, was once led by Christopher 'Bouncer' Hutch (25).
Hutch, a nephew of criminal mastermind 'The Monk', was also a suspect in the murder of drug addict Raymond Sallinger (40), who was gunned down in a Dublin pub in January, 2003.
One of Kinahan's close relatives is currently handling the affairs of the crime empire and earlier this year he launched a charm offensive on some of Dublin's most notorious gang bosses including Eamonn Dunne.
As part of his attempts to heal the rifts in Dublin's underworld, exiled Kinahan has arranged a luxurious, all-expenses-paid trip to Puerto Banus for Dublin's major crime bosses.
The summit meeting of Ireland's most feared gangland figures has also been arranged to organise a major shipment of drugs and arms destined for Ireland.
The Mediterranean love-in was reported to be Kinahan's latest attempt to cool tensions on the streets of Dublin after he organised a night out for his gangland associates at the Matthew Macklin fight at the National Stadium in Dublin last December.
Kinahan bought almost 50 tickets for the fight that were priced at €75 each, and crime figures like 'Fat' Freddie and Eamonn Dunne were in attendance along with other leading figures.
The purpose of the meetings was to stop in-fighting on the Dublin crime scene and to arrange a consensus around supply and pricing of drugs.
See PJ Browne, page 15