United's American owners, the Glazer family, launched a formal sale process late last year, with several bids received in February and March, but Zilliacus won't be placing another one.
"I have declined participation in a third bidding round for United," Zilliacus said on social media.
"The bidding is turning into a farce, with Glazers giving no respect to the club.
"The delays will make it very difficult for any new owner to build a winning team for next season."
Zilliacus was among several initial bidders including British billionaire Jim Ratcliffe, founder of chemicals producer INEOS, and Sheikh Jassim Bin Hamad Al Thani, the son of Qatar's former prime minister.
Sports industry news site Sportico reported this week that Manchester United would accept a third round of bids from prospective buyers at the end of the month.
The Glazers reportedly don't feel any offer made has been high enough yet and are waiting for a bidder to put more money on the table.
United are currently the fourth-richest football club in the world, according to Deloitte.