Uefa admit they will not be able to satisfy the huge demand for Champions League final tickets.
Many Liverpool fans will be without tickets for the final
Liverpool and AC Milan will each get more than 20,000 tickets for the 23 May final in Athens' Olympic Stadium.
There are plans for a fan park in the Greek capital, with giant screens, to cater for those without tickets.
But Uefa spokesman William Gaillard said: "Our advice to fans is not to travel without a ticket as we do not want them to be exploited by touts."
He added: "We know that however many tickets we provide it would never be enough - we could probably sell out a stadium with a million seats!
"But if supporters just want to savour the experience then they can use the fan park in downtown Athens."
Uefa, meanwhile, are not expecting trouble between the two sets of supporters.
Gaillard said: "There is no history of hostility between them and it gives us an advantage that we have the experience of these fans in a final in similar circumstances two years ago."