Officers are trying to liaise with family members to find out what they have planned, and where, and who might be coming from abroad to attend.
Garda intelligence has suggested there is a threat from the Hutch grouping against the cartel, although it is not clear how the attack might be carried out.
Senior officers are concerned that members of the Kinahan hierarchy abroad might travel home.
It is thought there is no information that Daniel Kinahan, elder son of cartel boss Christy, is going to fly back, with some senior sources doubting he will.
The military-style assault on the Regency Hotel in north Dublin on February 5, 2016, resulted in the death of Byrne, from Crumlin, south Dublin.
Daniel Kinahan was believed to have been the main target of the attack, but he escaped death.
That assault, involving gunmen dressed in SWAT-type uniforms and brandishing AK47s, was in retaliation for the murder of Gary Hutch in Spain the previous September.
Byrne’s death unleashed a murderous campaign by the Kinahan cartel, with the assassination of seven people here and another in Spain.
As it stands, it is thought the Byrne family is planning “low-key” events this Sunday, possibly including an anniversary Mass and a visit to Byrne’s graveside at Mount Jerome Cemetery in Harold’s Cross.
Gardaí are understood to be in contact with the Byrne family to try and determine what they have planned and who might be attending.
“This is to make sure the Hutch group don’t launch an attack,” said one source.
The funeral of Byrne, a 33-year-old father of two, was an extravagant affair, featuring ten stretch limousines and protected by a massive garda security operation.
The Armed Support Unit and the Special Crime Task Force, along with local gardaí, have been conducting checkpoints and patrols to prevent bloodshed.
They are taking in both Dublin’s north inner city — the home of possible Hutch targets — and the south west of the city, where most of the Kinahan members live.
It is thought all the main cartel targets, apart from those in custody, are still here, some of them openly visiting each other.
Fewer than six people in the wider Crumlin area, along with another senior lieutenant living in England, are considered to operate the top layers of the cartel in Ireland.
The cartel is under mounting pressure after a series of Garda successes against them.
Last Saturday, gardaí found an estimated €3m worth of heroin and cocaine, along with an assault rifle in Sallins, Co Kildare.
It is thought the drugs, linked to the cartel, were hidden inside sofas.
The previous Tuesday, gardaí uncovered 15 firearms, including a submachine gun, assault rifle, and silencers, in west Dublin.
The Friday before, gardaí and customs confiscated 1.9 tonnes of cannabis, worth an estimated €37m on the street.