The Bureau need to serve the mob boss in order to sell off a luxury Dublin mansion which they allege is owned and controlled by him.
His associate, Thomas 'Bomber' Kavanagh, was served earlier this month at Belmarsh maximum security prison, where he has been moved to for "security reasons".
It is the Bureau's case that both men took control of the property- 10 Coldwater Lakes in Saggart- after businessman Jim Mansfield Jnr failed to invest €4.5m for them.
This morning Shelly Horan BL, for the Bureau, said that efforts were still being made to serve a summons on Kinahan.
She said they were still looking for an appropriate address and asked for the matter to be adjourned until next month.
CAB have also been looking at whether Kinahan can be served via social media or through a business associate.
Ms Horan said that inquiries are ongoing to look for information regarding an appropriate address and said an update would be provided next month.
The court also heard that Thomas Kavanagh had been served with a summons in a UK prison earlier this month.
He is currently serving a 21-year sentence for drug trafficking and had been recently moved to Belmarsh prison, a maximum security facility, for "security reasons".
A Cab officer attended the prison and informed Kavanagh of the freezing order granted over 10 Coldwater Lakes and €5,000 cash found in an envelope with 'KAV 'written on it.
Thomas Kavanagh was also told that the matter was back before the court in Dublin today and asked if he had engaged with a legal representative.
The court heard he replied: "I don't want to talk to you go away."
Further efforts were made to notify Kavanagh of the hearing by the Metropolitan police this week.
The court heard that he replied "No comment" to several questions.
When asked if he would like to represent himself, he said: "I can't do that from here". He then refused to engage with the police officer who then left.
Mr Justice Michael McGrath put the matter back to June 21 for an update on service.
Evidence was given previously that in 2009, Jim Mansfield Jnr was handed two suitcases, containing a total of €4.5m, as part of the investments by the Kinahan cartel.
However, the Mansfield fortune "deteriorated" following the financial crash before going into receivership and the relationship "soured".
Ms Horan said that Kinahan and Kavanagh were then given the property and cash payments instead.
One cash sum of €5,000 was found in an envelope marked 'KAVS' in the basement of Tassagart House in Saggart, where Mansfield Jnr resided, during a search on January 29, 2015.
While the cash was "earmarked", nobody claimed ownership over the funds.
There were also separate sums of €24,150 and €20,500 recovered at different properties, understood to be attempts to repay the Kinahan and Kavanagh organised crime groups.
The barrister also said that 10 Coldwater Lakes was occupied and in the control of Daniel Kinahan from 2014. This belief was formed due to the nature of items linked to him discovered at the property.
The court heard that 10 Coldwater Lakes in Saggart was of historical interest to the Mansfield family but that it is controlled by the Kinahan cartel.
The Mansfield family had disavowed any interest in the cash with the Bureau now continuing its case against Kinahan and Kavanagh in relation to the west Dublin mansion.