Event executive Martin Kallen said hopes of hitting a 95 percent sales target for tickets would come up short – but could still reach the impressive levels of 93 or 94 percent.
He blamed poor demand from some countries for the shortfall.
With more than 1.1m tickets already sold, just 40,000 for the entire three-week tournament remain unsold.
Organisers say they will make one final promotions push in Portugal to sell the remaining tickets, but say they are satisfied with current sales figures.
Euro 2004 will fall short of its ticket targets – but with more than two months still to go more than one million tickets have so far been sold.
