Wilder's team achieves Premier League status, to always being the second most famous footballer in his sports-mad family.
"I'll never be more famous than the 'Big Dog'," Egan admitted. "He will always be number one. There's also my mum, I can't forget about her. As for us, we're just focusing on getting the job done."
The 'Big Dog', of course, is Egan's father, namesake and one of the greatest ever exponents of the Gaelic version of the game. A winner of six All-Ireland titles with County Kerry and countless individual awards, Egan snr was described as "a warrior" by fellow legend Pat Spillane following his passing seven years ago.
This weekend, which could see United promoted to the top-flight if they beat or draw with Ipswich Town, the former corner-forward's son hopes to write his own piece of history. But, as Egan admitted before training on Thursday, even delivering elite level football to Bramall Lane would pale into insignificance compared to his dad's accomplishments.
It is that sense of perspective, combined with the fact his mother Mary was a mean soccer player herself, which has helped the 26-year-old cope with the suffocating pressure of an automatic promotion race.
"Being from a sporting family has helped," Egan continued. "Growing up, I was obviously made aware of who my dad was at my young age.
"People in the UK won't know much about Gaelic football. But it is really big back there and he was really successful.
"Growing up, it definitely helped being in a sporting family. All I did every day was play sport.
"Not football all the time. I did Gaelic football, hurling. Pretty much anything.
"You develop a winning mentality, especially back home and in your home town. You are playing for your own parish and it has helped my career."
Egan spoke to his mum, a League of Ireland winner with Cork Rangers, earlier this week as preparations for tomorrow's meeting with Ipswich intensified. Second in the table and three points ahead of Leeds with only two matches remaining, United will effectively be up if they overcome their already relegated opponents by virtue of a vastly superior goal difference. Marcelo Bielsa's side, who face Aston Villa on Sunday, have scored four fewer goals and conceded seven more.
Egan, the Republic of Ireland centre-half, has emerged as a key member of a defence which has kept 20 clean sheets so far this season since becoming United's record signing last summer. Two of those came during the Bank Holiday victories over Nottingham Forest and Hull City. Allied with a prolific attack and Leeds' faltering form - they lost to Wigan Athletic and Egan's former club Brentford over the Easter period - it has proved an irresistible combination.
"I left a good club and a really good team," he said, tracing his journey from West London to South Yorkshire. "We only just missed out on the play-offs. I knew Brentford had a really good team. From playing against Sheffield United, I knew they had a really good team.
"One of the toughest games I had personally last season was against Sheffield United. As soon as the manager made his interest clear, I really felt this would be a good fit. That I could come here and do well."
Although the momentum has swung in United's favour, manager Chris Wilder has been at pains to point out that nothing has been decided yet. Indeed, analysing Ipswich's credentials earlier this week, one could have been forgiven for thinking he was describing a club also on the verge of promotion rather than searching for only its fifth league win of the campaign. Still, as Wilder reminded, his opposite number Paul Lambert remains a formidable adversary and the visitors can now approach the fixture with a freedom denied to United, Leeds and leaders Norwich City.
"Nothing is a given in football but, thankfully, it has gone as well - or better - than expected," Egan said. "I was asked why I came here at my first interview and I just felt something good was happening. I wanted to get promoted.
"I have kept that belief through the whole season. We have a really good squad, talented players who I felt I could add to. The manager, as well, has proved his success as well. I really wanted to come here."