The Taoiseach says it would be entirely appropriate for sporting and media organisations to have nothing to do with the proposed meetings of Tyson Fury and Anthony Joshua.
Daniel Kinahan played a key role in brokering the deal.
Earlier in the week, Varadkar said that they Department of Foreign Affairs would be in contact with the United Arab Emirates authorities regarding Kinahan's role in proceedings.
However, addressing the Dail on Friday, the Taoiseach conceded there is little the Irish government can do to stop the fight going ahead.
Kinahan was previously named in the High Court as being a senior figure in organised crime on a global scale.
Varadkar told the Dail that the UAE, "know our concerns and our problems with it".
"It is not a decision for me", he added, "but I think it would be entirely appropriate for sporting organisations or media organisations to have nothing to do with this.
“They maybe don’t know the facts or don’t know the truth but they need to know them. I wouldn’t like to see them getting any attention at all given the circumstances."
Fine Gael TD Neale Richmond has written to both Sky Media chief executive Stephen van Rooyen, and BT Ireland managing director Shay Walsh regarding the fight.
Mr. Richmond addresses both by saying, "I would relish the opportunity to watch Tyson Fury take on Anthony Joshua and I am sure it will be a much sought after broadcast.
"However, I feel it is your duty as a broadcaster, if you do aspire to broadcast this proposed fight, to truly familiarise yourself with the actions of Daniel Kinahan.
"Are you comfortable with your company being associated with such an individual?"
— Neale Richmond (@nealerichmond) June 11, 2020
In response to a similar inquiry from Associated Press journalist Rob Harris, BT Sport responded with the following:
"BT Sport is not currently involved in the Tyson Fury and Anthony Joshua negotiations.
"Our broadcast agreement for the fights of Tyson Fury is exclusively with Frank Warren's Queensberry Promotions. We have had no dealings with MTK or any of their representatives for this fight.
"BT reviews all sports rights and broadcast deals with the appropriate levels of responsibility and scrutiny before deciding on a course of action.
"We cannot comment further on a potential fight which to the best of our knowledge is not confirmed, and which has not been offered to us."
Tyson Fury confirms he's agreed a two-fight deal with Anthony Joshua in 2021.
First, he will finish the trilogy with Deontay Wilder. pic.twitter.com/gBVtMsGVWm
— Boxing on BT Sport 🥊 (@BTSportBoxing) June 10, 2020
BT Sport's boxing-based Twitter repurposed Fury's video announcing the fight earlier this week, wherein Kinahan is name-checked a number of times.