Contrary too many, I don't believe its to re-establish the USSR.
Its a convenient answer of course, but all that territory helped bring down the USSR and the Imperial Russian Empire prior to that. A few of those old republics were all intents and purposes leeches to thier treasury and production.
I won't go into details as I'll get flamed angrily here. But its fairly clear Putin had every intention of invading and eating a portion of Ukraine for a VERY long time. Forgot when, but he told the Polish government once he got the piece he thought belonged to them, he would turn a blind eye of them taking what used to be there's. Poland politely declined.
Another issue, our unbridled support for the drunkard Yeltsin. My understanding is that its still a major embarrasment over there. Ironically, our support of him got the USA to basically "sign off" on making a non-descript, unassuming and appeared lacking ambition former KGB agent who was only a mayor with no major accolades into a Vice President. That being of course Putin.
Again, there are more reasons, but it will be like the Cuban missile crisis. All the reasons won't come out until much later.