Three planeloads of the fans were due to fly to the Ukrainian capital, where the match is being staged on Saturday night, but Kiev airport says it does not have enough landing slots.
Liverpool say the problem arose as a result of a dispute between the travel company and the aviation authorities in Kiev over the size of the aircraft.
World Choice Sports, which organised the trips, said on its website: “With deep regret, we have had to cancel three flights to Kiev.
“Due to so many flights going into Kiev, Kiev Borispyl has [been] unable to allocate times for aircraft.
“We have worked extremely hard over the last 48 hours trying to resolve these issues. We have had Liverpool Football Club, police, UEFA and everyone at the highest levels of authority trying to resolve this.
“We have exhausted all avenues to try and get landing slots. We have had them from Liverpool airport and Manchester Airport and we have applied for slots in the correct manner and timeframe with the authorities. To reiterate, this problem IS with Kiev.”
The firm said the return flights affected were: out 25 May ET8700 and back 27 May ET8701; out 26 May ET8704 and back 27 May ET8705; and out 26 May ET8706 and back 27 May ET8707.
The statement added: “At this stage we can only make a huge apology and are very sorry [to have] let you down on this occasion. We will be processing full refunds of monies paid as soon as possible, starting tomorrow.”
Liverpool said they were continuing to try to resolve the problem.
A club statement said: “Liverpool Football Club is continuing to work with all of the relevant stakeholders in the UK and Ukraine in an attempt to resolve a situation which has left around 1,000 fans without flights to Kiev for the Champions League final.
“Flights chartered by World Choice Sports had been set to take supporters to Ukraine, but a dispute between the Widnes-based travel company and the aviation authorities in Kiev over the size of the aircraft has led to the trips being cancelled.
“Along with officials from Liverpool John Lennon Airport, Liverpool City Council, UEFA and the authorities in Kiev, Liverpool FC has been endeavouring to resolve the issue since it first came to light and will continue to do so until all avenues have been exhausted.”
Liverpool mayor Joe Anderson said he was working directly with Kiev mayor Vitaliy Klychko to sort out the issue.
“Thank you for your help & support. Close to solution now and more details will follow soon,” he said on Twitter.
Anyone trying to sort out replacement tickets could find their trip expensive – a web search of major web-based travel agents by Sky News found there were no return flights left from the UK to Kiev leaving on Friday for less than around £1,200.
Fans reacted with anger at the announcement on Twitter, with many blaming UEFA for choosing a city that did not have as many travel connections as other bigger European capital.
Others asked for help, like Raf B, who tweeted: “My 18 year old son’s flight to Kiev just been cancelled by World Choice Sports. He is devastated. Anyone got a seat on a private plane?! @LFC”
The team itself successfully set off from Liverpool John Lennon Airport for Kiev on Thursday afternoon ahead of Saturday’s match against Real Madrid.
UEFA has issued a leaflet telling fans how to get to the NSC Olimpiyskiy Stadium for the 9.45pm (local time) start.
It says Kiev’s main Borispyl airport has “good connections to most European hubs” and a free shuttle bus will take people on to the metro system.
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In the absence of flights to Borispyl, it recommends flying to Zhulyany airport, on the outskirts of Kiev, which handles a sixth of the passenger traffic of the main airport, or flying into other Ukrainian or Polish cities and travelling by rail or car.
On Wednesday, the Champions League final itself was threatened with disruption when a Ukrainian state security agency said the Russian government was preparing an enormous cyber attack on the event.