Out of curiosity - why do you think Russia has never tried?
First russian president Boris Yeltsin applied for membership (strictly speaking, consulted about "possibility to join") in NATO and EU (1991) and was rejected.
With EU the sticking point was banking. Since rouble was very weak, opening banking to EU would mean a takeover and loss of financial independence.
With NATO the sticking point was the size of USSR and NATO fears of too much influence. NATO feared that USSR military would absorb all other european forces. Sort of reverse of banking situation for EU.
Sources