The Russian president was speaking to the BBC amid claims Downing Street had tried to encourage Moscow to oppose Scottish independence - which Number 10 has denied.
He also refused to rule out an independent Scotland becoming part of Russia's new customs union.
Mr Putin, whose own government is faced with secessionist bids, said every people had a right to self-determination.
However, he added: "One should not forget being part of a single, strong state has some advantages and one should not overlook this. It's a choice for each and every people according to their circumstances."
Asked, with a smile, if he might persuade Scotland to become a member of Russia's new customs union, he replied, also with a smile: "I wouldn't rule that out."
Itar-Tass, the Russian state news agency, said over Christmas: "Great Britain is extremely interested in the support of Russia, as holder of the G8 presidency, in two vital areas in 2014: the Afghan pull-out and the Scottish independence referendum." It cited an anonymous source in the office of Prime Minister David Cameron as the basis of its report.
First Minister Alex Salmond responded, saying that if the news agency's report were accurate "Westminster has been caught red-handed trying to stir up hostility to Scotland instead of representing Scotland's interests."
No 10 was dismissive, stating: "There has been no approach to the Russian Government for help in the independence referendum and there won't be one. Any suggestion the UK Government has asked President Putin to help win hearts and minds in the referendum is ridiculous."