The centre-half, who kick-started his career with Gillingham before becoming Bramall Lane's record signing last summer, was speaking as United's preparations for the new Premier League season continue to gather pace.
Egan, a key member of the squad which finished second in the Championship last term, said: "Our team is full of players who've played in League One, even League Two. There is nothing wrong with playing in League One or League Two, but it shows you the quality is there in those leagues."
Egan spent last week at a Republic of Ireland training camp in Portugal ahead of next month's Euro 2020 qualifiers against Denmark and Gibraltar. United team mates Enda Stevens and David McGoldrick, who found himself without a club last summer after being released by Ipswich Town, have also been called-up by Mick McCarthy.
Stevens, who forced his way into the international set-up after joining United from Portsmouth, was once deemed surplus to requirements by University College Dublin before heading to St Patrick's Athletic and Shamrock Rovers.
"We have players like Didsy (McGoldrick) who has obviously played Championship most of his career," Egan continued. "Didsy came to us on trial because the Ipswich manager didn't fancy him or whatever, and he's gone on to be our player of the season in a promotion-winning campaign.
"That just shows what can happen if you've got the ability and you continue to believe in yourself."
United hope to make a number of new signings before embarking upon their first top-flight campaign since 2007, with former loanee Dean Henderson among Wilder's list of targets. The goalkeeper has told Manchester United he wants to return to South Yorkshire next term, albeit on a temporary basis, with officials at Old Trafford expected to grant his request after handing him a new contract.