I mean, anything is possible, and there's certainly a wealth of data on Twitter that Google would love to mine (not to mention a lot of identity management that Google would love to pull into its products).
(One serious downside to such an acquisition would be Twitter-haters crowing that means Twitter will be gotten rid of, and Google+-haters doing much the same for that platform.)
That said, these sorts of rumors fly way too freely, and I wouldn't make any plans about it until it should come to pass. Indeed, the only folk who should be giving it any planning at all are the people over at Facebook.
(h/t +steph wanamaker)
Google ‘looking at buying Twitter’
Twitter shares jump on reports Google has approached the social network about a possible takeover