Never ever that was a thing. There has never been any applications to have Russia as NATO member. What Putin was referring and had in mind was not exactly NATO membership but special treatment to Russia, that would allow using benefits of NATO, by not submitting to anything.
the rabbit hole goes a bit deeper, and it seems that ruskie were trying to knock the doors since as early as 1954 and were repeatedly told to duck off
i have not found the proofs for the part "would allow using benefits of NATO, by not submitting to anything" - the closest to this was the request to accept them sooner
