Uefa is urging Liverpool fans in Athens not to buy tickets for the Champions League final from touts.
Counterfeit tickets are being sold for thousands of pounds
British police warned fans about 5,000 counterfeit tickets are in circulation.
Uefa spokesman William Gaillard told BBC Radio Five Live: "We don't want fans to pay enormous sums for tickets that may not get them in the stadium.
"Don't buy them - the risk is too big. It is illegal in Greece so you risk being arrested and secondly these tickets may not be valid tickets."
Up to 40,000 Reds supporters are expected to attend the match.
Each team has been allocated 17,000 tickets in a stadium with a capacity of 63,000, with more than 20,000 set aside for other groups.
But Uefa dismissed criticism of its distribution of the tickets.
Gaillard added: "We knew there would be a lot more Liverpool fans in Athens than tickets available. There was in Istanbul in 2005 and it would be true anywhere in Europe.
"Stadiums have a certain capacity. Even if we were playing in a larger stadium like Barcelona we would still have probably 10,000 or 15,000 fans without tickets.
"It's very sad but it's a fact of life."
Gaillard played down hopes of some extra tickets being made available because of an Italian air strike that could prevent some Milan fans from travelling to Greece.
He added: "We have been told by AC Milan that a few fans have been affected by the strike, but since the strike was announced over two weeks ago they have been re-routed so they can make the game.
"Less than 1,000 could have been affected.
"In the final days before a Champions League final the demand for tickets is very high and there a number of myths flying about
"I heard this morning that 4,000 tickets were available from Milan fans that were returned by the club, but I can assure you this is a complete myth - they have used up all their tickets.
The senior British officer advising the Greek authorities, Chief Superintendent Dave Lewis, of Merseyside Police, has pleaded with ticketless fans not to travel.
He said: "I'm a realist. I've been asked for tickets while walking around. I expect the neutral east stand will be predominantly full of Liverpool supporters.
"But I would urge fans who cannot find tickets not to go to the ground, they make matters worse for those with legitimate tickets - they will create problems for their own kith and kin."
There has been resentment that the allocations to the two clubs have been so low, driving many supporters on to the black market.
Fans said locals were asking them for 1,500 euros (£1,024) for tickets, down from 2,500 euros (£1,706) the previous day.
A British man was in custody for allegedly selling forged tickets worth 58,000 euros (£39,400) to an Italian travel agent, and two Britons were hospitalised after a fight over buying tickets.