He distanced himself one week after reports suggested the UK Government was seeking Russia as an ally to stop Scotland leaving the union in a referendum this September.
The claim was dismissed as ridiculous by Downing Street at the time.
Mr Putin told the BBC's Andrew Marr Show: "It's not a matter for Russia, it's a domestic issue for the United Kingdom."
People have the right to self-determination, he said.
"But I believe one should not forget that being part of a single, strong state has some advantages and one should not overlook this," he continued.
"It's a choice for each and every people according to their own circumstances."
Asked if an independent Scotland could join a customs union with Russia, he said: "I wouldn't rule that out".