On Thursday, officials said Russian soldiers could even launch a new assault on the capital, Kyiv.
As the invasion enters its third month, Putin's troops have withdrawn from a number of cities and are focusing their efforts on eastern Ukraine, mainly in Donbas.
“[If] the Russians have concentrated sufficient force such that if they were to use it intelligently, they might be able to surround and destroy a very significant portion of Ukraine’s armed forces - some of its best forces - and make territory, which would be very difficult to dislodge," a Western official said.
"In a really worst-case scenario, they might then be able to look again at whether they could revisit some of their pre-war objectives, potentially renew an attack on Kyiv, or to attempt to take Odesa and deprive the rest of Ukraine from access to the sea."
They added that, should Putin achieve any one of those objectives, it would be seen as "success" for the Russian president, whose invasion of Ukraine thus far is widely viewed as not having gone to plan.
"Consolidating his control over the Donbas, the whole of the Oblasts, Crimea, and the land bridge between them would certainly be something that would be seen to be, or could be seen to be, a success," they said.
"That is still something which is potentially within reach if the Russians are successful in the campaign in the Donbas."
On Thursday, Putin claimed victory over the south-eastern Ukrainian city of Mariupol. However, Ukrainian president Volodymyr Zelenskyy said Ukrainian troops remain in a part of the city.
Earlier this month, the UK refused to rule out Nato involvement in Russia if chemical weapons were used.
It comes as the UK's Ministry of Defence warned Russia could intensify their campaign in the coming days in order to try and show some success ahead of the country's Victory Day celebrations.
A UK government spokesperson tweeted in an update: "Russia likely desires to demonstrate significant successes ahead of their annual 9th May Victory Day celebrations.
"This could affect how quickly and forcefully they attempt to conduct operations in the run-up to this date."
Elsewhere, according to Bloomberg, Kremlin officials are becoming increasingly worried the Russian president could use limited nuclear weapons in their ongoing assault on Ukraine.
Bloomberg also reported there is no sign Putin will change his mind, and that the Russian president faces no direct challenge in the Kremlin.
Watch: Ukraine war: Why is Mariupol so important to both sides?