'I certainly hope she's not the future and I don't believe she is, ' Lieberman said in a Fox Business Network interview.
On Sunday, Lieberman called Ocasio-Cortez's reaction on Twitter "kind of silly".
Lieberman, 76, represented CT in the US Senate from 1989 to 2013.
"New party, who dis?"
"Who dis?" is a common response (mainly used by millennials) to a text message from an unknown number.
Since upsetting six-term incumbent Joe Crowley in a primary last summer and winning election to Crowley's old seat in November, Ocasio-Cortez has used her vast social-media following to chastise fellow Democrats she believes are insufficiently progressive and too beholden to the antiquated establishment. "But if you look at the majority of new Democrats in the House, they tend to be, I say, center-left, if they are not left-left".
Price-tag estimates for carrying out that agenda - costs that taxpayers would bear - range from $2 trillion to $51 trillion.
Ocasio-Cortez was denied a seat on the influential Ways and Means committee this week despite a public pressure campaign launched by progressive advocacy groups.
'More, please, ' a Republican Senate aide told DailyMail.com on Friday.
Incumbent Democrats are most annoyed by Ocasio-Cortez's threat to back primary opponents against members of their ranks she deems too moderate.
Ocasio-Cortez followers were there to applaud the tweet, supporting the idea of Lieberman and his views being out of date with even more jabs and memes. And establishment Democrats are beginning to become annoyed with her. But their frustration goes beyond that: Democratic leaders are upset that she railed against their new set of House rules on Twitter the first week of the new Congress. Lacy Clay (D-Mo.), a senior Financial Services Committee lawmaker "Time will tell, and this one term will tell us a lot about her abilities as a legislator".