The Fine Gael candidate and former Olympic boxer bought them while engaged in a drunken bidding war at an auction.
The 32-year-old told how he was initially embarrassed when he woke up the next day with a hangover and a very expensive pair of shorts.
But he grew to love them, and they now take pride of place in his house alongside a pair of tickets for the 1960 Olympics.
As well as winning silver at the Beijing Olympics, Egan has 10 Irish boxing titles. He secured a European bronze in 2006 and again in 2010, but he hung up his gloves last year after he was beaten by Joe Ward.
Egan may need Ali's boxing shorts to be in with a fighting chance of winning the local elections for Fine Gael.
Not content with having won an Olympic medal, the 32-year-old Dubliner made headlines in recent weeks after he announced his intention to run for a council seat in Clondalkin. He also attracted media attention after he admitted he had considered joining rivals Fianna Fail.
But Egan claimed he eventually opted for Fine Gael because he wanted to "keep it real".
"As with my sporting career, I have always aimed for success, and if elected I will bring the same energy to working for my community," he said.
His toughest battle in life was with his alcohol addiction, which he has openly spoken about in the media.