They say one potential cause of the illness could be adenoviruses, but they haven't ruled out Covid-19 as a cause.
Officials are examining 49 cases in England, 13 in Scotland and 12 across Wales and Northern Ireland.
The UK Health Security Agency (UKHSA) said parents should be on the lookout for symptoms such as jaundice.
Dr Meera Chand, director of clinical and emerging infections at UKHSA, said officials were looking at a wide range of possible factors which could be causing children to be admitted to hospital with liver inflammation.
"One of the possible causes that we are investigating is that this is linked to adenovirus infection. However, we are thoroughly investigating other potential causes," she said.
Other possible explanations being investigated include Covid-19, other infections or an environmental trigger.