WBC champion, Tyson Fury has recently thanked Daniel Kinahan for brokering a deal that would allow him to fight Anthony Joshua in 2021 – as long as he defeats Deontay Wilder.
Daniel Kinahan has no convictions but has been named in court by a judge as a senior figure in Irish organised crime.
Mr Varadkar told parliament he was “taken aback” by Fury’s comments given that they referred to someone with a “chequered history”.
He confirmed there had been contact on the matter between the Irish Department for Foreign Affairs and the UAE – where it has been suggested the bout could be held.
His government would raise the issue with broadcasters intending to air the event, added Mr Varadkar.
In an Instagram video posted on Wednesday, Fury said the clash was going ahead, offering “a big shout-out… to Dan” for his efforts.
“I’m just after getting off the phone with Daniel Kinahan,” said the boxer.
“He’s just informed me that the biggest fight in British boxing history has just been agreed.”
The development is widely seen in Ireland as the latest example of Daniel Kinahan attempting to launder his reputation in the UK and internationally.
The Criminal Assets Bureau – part of the Irish police, the Garda Síochána – has said he “controlled and managed” the operations of the family crime syndicate and “has associations that facilitate international criminal activity in Europe, Asia, the Middle East and South America”.
In November 2019, Europol identified the gang linked to Mr Kinahan as one of the main cocaine importers in Europe, adding that it now smuggled its surplus supplies to countries as far away as Australia.
The Irish Daily Star tabloid has said it will refuse to publicise the fights, which are expected to generate huge money and interest if all the details can be finalised.
In an editorial on Thursday, the paper said: “The fact that (Daniel Kinahan) has been hailed as some sort of saviour of boxing is not only a sad indictment of the sport but an insult to the thousands of lives he has helped ruin.”
Media coverage in Ireland to Kinahan and the proposed fights is very different from that across the Irish Sea, where Mr Kinahan is merely described by some as “a controversial figure”.
Meanwhile, Daniel Kinahan first came to widespread public attention in Ireland in February 2016 when gunmen attacked the weigh-in at a boxing bout that resulted in the murder of a man described as a leader of the Kinahan crime cartel in Ireland.
The immediate aftermath of the shooting as spectators fled in fear was caught on camera and the footage went around the world.
It is believed he was the intended target. The murder was part of a feud that has claimed at least 18 lives.
Politicians, police officers and the public in Ireland are keen that the outside world gets to know what they call the real Daniel Kinahan.