Sky News says Tuesday's event will not go ahead unless Boris Johnson accepts its invitation.
The 81-year-old is "over the worst" and "talking", former Home Secretary Alan Johnson says.
Minister Tobias Ellwood says opponents of a no-deal Brexit "have the numbers" to threaten the government.
The EU Commission asks why many EU citizens were unable to vote in the UK.
The proposal is aimed at avoiding checks on the Irish border after Brexit, but could face major hurdles.