Putin calls his invasion a "special military operation" to disarm Ukraine, defend its Russian speakers and prevent Kyiv cosying up to the West.
When his forces entered Ukraine on February 24, Moscow's media regulator banned outlets from describing the attack as a "war" or "invasion".
Declaring war would enable the Kremlin to call up more conscripts, and keep them beyond their usual one-year term, as well as impose martial law to shore up its economy and close the country's borders.
It would also mean Moscow could call on its international allies, such as Belarus, to offer more support.
Wallace said yesterday Putin could announce the mass mobilisation of Russians.
"He is probably going to declare on May Day that we are now at war with the world's Nazis and we need to mass mobilise the Russian people," Wallace told LBC.
Security experts at the Royal United Services Institute also said it had become increasingly likely Putin would use Russia's military day to officially frame his "special military operation" as a "war".
A Western official said Putin could also announce the declaration on May 9 in order to build further support for his operation in Ukraine.
"There is a possibility we see a greater call to arms and one could set out a thesis that it's a day of patriotism and this is a moment for the Russian people to get behind this operation," the source said.
Muddy conditions, poor intelligence and old maps have plagued Russian troops in their new push to take the Donbas region, Western officials said.
It came as a captured British fighter, Andrew Hill, 35, was paraded on Russian television with serious injuries.
The British Foreign Office confirmed that Scott Sibley, 36, a former British soldier, had been killed in Ukraine, and another Briton had gone missing.
Separately, two British volunteers - Paul Urey, 45, and Dylan Healy, 22 - who were providing humanitarian aid in Ukraine - were captured by the Russian military.
The Prince of Wales also spoke out on the conflict yesterday, saying it was a "stark reminder" that there could be "no substitute for credible defence".