Mr Varadkar was responding to a question relating to Ireland’s historical foreign policy.
He said he did not believe an Irish delegation would be present at the Russian president’s funeral.
The hypothetical situation relates to events almost 80 years ago.
The Irish Government adhered to a strict policy of neutrality throughout the Second World War.
However, then-taoiseach and minister for external affairs Eamon de Valera sparked outrage among the international community when he expressed condolences to Germany’s Irish minister Eduard Hempel following Adolf Hitler’s death by suicide in 1945.
The event caused significant reputational damage to Mr de Valera and the state, and is regarded as an important moment in the history of Irish neutrality.
The diplomatic conundrum was dragged into the 21st century this week at a post-Cabinet briefing with Mr Varadkar.
While Ireland insists it continues to employ a policy of neutrality, senior government ministers say this relates to being militarily neutral rather than being politically neutral.
Last week, Mr Varadkar pledged to stand with Ukraine for as long as it takes when he visited Ukrainian President Volodymyr Zelensky in Kyiv.
He also announced millions of euro in additional funding for humanitarian aid to Ukraine.
Following the trip, the taoiseach was questioned about Mr de Valera’s actions following the death of Hitler.
Asked by reporters if Ireland would offer a similar condolence to Russia in the event of Mr Putin’s death, Mr Varadkar said: “I don’t think so.”
Briefly pausing to consider the theoretical event, he added: “It’s a good question, I hadn’t thought of it before.”
Mr Varadkar, who was banned from travelling to Russia last year, concluded: “I wouldn’t imagine we’d be represented at the funeral.”
In November, the Kremlin said it was placing 52 “key representatives” from Ireland on a sanctions list for expressing what it claimed was Russophobic sentiment.
Mr Varadkar was among the officials subjected to the ban by Russia.
The Russian embassy in Dublin has been approached for comment.