While decades-long tradition dictates that the winner of the contest gets to host it the following year, organisers said the security guarantees required to hold the competition meant discussions would be held with the runner up, the UK.
Ukraine was not happy with the decision, with Culture Minister Oleksandr Tkachenko, on Telegram, demanding more negotiations "because we believe that we will be able to fulfil all the commitments we have made".
The UK's entry to the contest last month in Turin, Space Man by British singer-songwriter Sam Ryder, came second behind Ukraine's Kalush Orchestra after a string of lowly finishes.
The group rode a wave of public support to claim an emotional victory with Stefania that was welcomed by the country's president.
Organiser the European Broadcasting Union (EBU) said it was in discussions with UK broadcaster the BBC to host the next event.
"The EBU... share their sadness and disappointment that next year's contest cannot be held in Ukraine," the Eurovision Song Contest said.
"It is our full intention that Ukraine's win will be reflected in next year's shows."
The event normally draws a television audience of close to 200 million.
"We would be committed to ensuring that it overwhelmingly reflects Ukraine's rich culture, heritage and creativity as well as building on the ongoing partnership between our two countries," a spokesman for UK Prime Minister Boris Johnson, who was visiting Kyiv on Friday, said.
The BBC said: "Clearly these aren't a set of circumstances that anyone would want... we will of course discuss the BBC hosting the Eurovision Song Contest."
The last time the UK hosted the annual competition was in 1998 when it was held in Birmingham after British rock band Katrina and the Waves' song Love Shine a Light won the year before.
