The event is being staged for the fourth successive year at a bog in Doohamlet, near Castleblayney.
Cavan/Monaghan Fine Gael Dáil deputy Sean Conlan revealed that Mr Varadkar had accepted his invitation to attend the quirky event.
“He has also indicated that he will be likely to take part in the event — the first government minister ever to do so,” Mr Conlan said.
“Minister Varadkar sees this as a novel tourism attraction, because of the unique nature of the muddy challenge.”
Meanwhile, Declan Connolly, spokesman for the organisers, said: “We hope to set a new Irish world record this year for speed-swimming in the mud.”
Overall, more than 150 contenders are expected to participate in the all-day event.
One Dublin contender, Kevin Cooper — who chalked up a record time last year — is tipped by the bookies to retain his “muddy” title.
Funds from this year’s event will go towards the treatment of a young Co Monaghan boy, Cian Connolly, who is battling cancer.