Gardaí believe it is "highly unlikely" that Sean McGovern will travel back to Dublin for fear of being detained.
The on-the-run cartel member is wanted here to face murder and organised crime related charges linked to the Hutch/Kinahan feud that claimed 18 lives.
A warrant was issued for McGovern's arrest earlier this year, but he is currently believed to be based in the Middle East.
Over the weekend his father, Desmond McGovern, passed away at his Crumlin home.
Sources said that Mr McGovern was a "highly respectable" man who previously worked with the Eastern Health Board.
His funeral is set to take place on Thursday morning at the Our Lady of Good Counsel church on Mourne Road in Drimnagh.
A death notice described him as a beloved husband and devoted dad who "will be forever loved and very sadly missed" by his family and friends.
Independent.ie understands that detectives will monitor the funeral service to determine if Sean McGovern (36) has returned for his father's funeral.
However, gardaí believe it is "highly unlikely" that he will travel back to Dublin for fear of being detained.
One source said: "He is facing very serious charges and would be arrested on sight if he returned to Ireland. All the intelligence indicates that he has no intention of travelling back here because of this.
"While the probability is highly unlikely, gardaí cannot take any chances and will be keeping a watching brief of proceedings. This will be done discreetly," the source added.
Sean McGovern is wanted to face charges of murder and directing a criminal gang relating to the fatal shooting of Noel 'Duck Egg' Kirwan in December 2016.
Gardaí also want to charge McGovern in relation to a failed plot to murder Hutch associate James 'Mago' Gately in Belfast in April 2017.
Detectives believe he played a "hands on" role in organising attacks between 2016 and 2017 but later fled to the Middle East.
From there he is suspected of continuing to play a vital part in the cartel's operation and was in charge of running the European drug network prior to the announcement of financial sanctions against the gang by the US Government.
Speaking at a press conference in Dublin earlier this year Assistant Garda Commissioner John O'Driscoll, now retired, said they were appealing for information on McGovern's movements.
“Anyone who has knowledge of the whereabouts of Sean McGovern, who is subject to a European Arrest Warrant to contact An Garda Siochana.”
The 36-year-old Crumlin native was also injured at the Regency Hotel shooting in February 2016.
He suffered a gunshot wound to the stomach but was discharged from hospital several days later and refused to assist the garda probe.