"Truthfully, we believe Chris Byrd posed unique challenges to the style of Lennox Lewis."
Hornewer, who had an acrimonious split with Lewis, added: "Now that he has taken himself out of the picture we will turn our sights to a true champion, Evander Holyfield, who many observers believe bested Lewis in their last fight."
Holyfield and Byrd, both promoted by Don King, are already set to contend the vacant IBF championship, possibly in Las Vegas on 14 December.
Lewis has yet to officially confirm that, at the age of 37, he will fight on. But his American television backers, HBO, are keeping 7 December free for a WBC title defence against 26-year-old Ukrainian Vitali Klitschko.
If, as expected, he wins that clash, Lewis would then go on to a lucrative rematch with Tyson before signing for a summer showdown with Vitali's brother, Wladimir, who most observers regard as the best of the new generation of heavyweights.
Explaining his decision to return the IBF championship, Lewis said: "My team and I had already determined that there was no public interest in a Lennox Lewis-Chris Byrd bout.
"The fact is that the champion makes the belt important, not the other way around."