Foreign secretary Liz Truss made the comments after US president Joe Biden suggested moving to penalise the Russian leader could be an option in the case of an invasion.
When asked on Tuesday if he could see himself sanctioning President Vladimir Putin in those circumstances, Mr Biden told reporters: “Yes, I would see that.”
On Wednesday, Ms Truss told ITV News the UK government had not ruled out supporting such personal sanctions.
"In fact, we're looking at sanctions on both individuals and institutions in Russia, we're shortly going to be introducing legislation to bring in tougher sanctions," she said.
Boris Johnson said on Tuesday that Britain was prepared to deploy troops to protect Nato allies in Europe should Russia invade Ukraine, as he warned Mr Putin faced “ferocious” Ukrainian resistance.
Ms Truss added: "We've been at the forefront of supplying Ukraine with defensive weapons and we've trained up 20,000 Ukrainian troops. We're very clear with Russia that the Ukrainians will fight back if Russians stage an invasion."
The UK is open to supporting personal sanctions against President Putin, Liz Truss says
The prime minister also said on Tuesday the UK and its allies stood ready to impose “heavy economic sanctions” on Russia and voiced fears that any invasion would result in “bloodshed comparable to the first war in Chechnya or Bosnia”.
Mr Johnson told the House of Commons: “If Russia pursues this path, many Russian mothers’ sons will not be coming home.
“The response in the international community would be the same and the pain that would be inflicted on the Russian economy will be the same.”
He made an appeal for diplomacy to resolve the tensions and avoid a war that would “earn and would deserve the condemnation of history”.
Labour leader Sir Keir Starmer said on Tuesday his party “stands resolute” in supporting Ukraine’s independence and sovereignty.
Mr Johnson, making a statement to the Commons, went on to say: “The British Army leads the Nato battle group in Estonia and if Russia invades Ukraine, we would look to contribute to any new Nato deployments to protect our allies in Europe.”
A Russian invasion of Ukraine could see the worst bloodshed since WWII, Boris Johnson tells MPs
He also told MPs the UK could not “bargain away” the vision of a free Europe which emerged between 1989 and 1991, adding: “We will not reopen that divide by agreeing to overturn the European Security Order because Russia has placed a gun to Ukraine’s head, nor can we accept the doctrine implicit in Russian proposals that all states are sovereign, but some are more sovereign than others.
“The draft treaty published by Russia in December would divide our continent once again between free nations and countries whose foreign and defence policies are explicitly constrained by the Kremlin in ways that Russia would never accept for herself.”
He went on: “There is nothing new about large and powerful nations using the threat of brute force to terrify reasonable people into giving way to otherwise completely unacceptable demands.
“But if President Putin was to choose the path of bloodshed and destruction, he must realise that it’d be both tragic and futile, and nor should we allow him to believe that he could easily take some smaller portion of Ukraine – to salami-slice – because the resistance would be ferocious.”
Russian troops have massed at the border with Ukraine and intense diplomatic activity has failed to ease tensions.
Sir Keir said: “For too long the implicit message to Moscow has been that President Putin can do what he likes and the West will do little to respond.
“We must now change course and show Russia that any further aggression will result in severe real-world consequences.”