There is an interesting transcript of what Putin said to US President Bush in 2001.

"Let me return to NATO enlargement. .... Russia is European and multi-ethnic. I can imagine us becoming allies. Only dire need could make us allied with others. Bit we feel left out of NATO. IF Russia is not part of this of course it feels left out. Why is NATO enlargement needed? In 1954 Russia applied to join NATO. I have the document. [ Bush: "that's interesting" ] NATO gave a negative answer with four specific reasons. Lack of an Austrian settlement. The totalitarian grip on Eastern Europe. And the need for Russia to cooperate with the UN disarmament process. Now all these conditions have been met.Perhaps Russia could be an ally."