"The animal spirits are up in that general area," Cashin said on "Squawk on the Street," referring to social media stocks and Friday's initial public offering of Zulily, an online retailer of women and children's clothing, on the Nasdaq. The IPO comes a week after Twitter went public.
(Read more: Shares of online retailer Zulily soar in debut)
By afternoon, shares of the Seattle-based company were up more than 70 percent, pushing the company's value at about $4.6 billion.
"I just worry a little bit that we are edging back to the 'eyeball-and-click' thing we had just before the year 2000," said Cashin, UBS' director of floor operations. "It's not quite frothy yet, but it won't take that much stirring to get there."
(Read more: These Web companies 'don't make sense': Pro)
Tom Porcelli, chief U.S. economist for RBC Capital, had a different take, saying he was not concerned about a bubble and that the consumer space seemed "depressed."
He said improvements in credit markets would help spur economic growth going into 2014.
"I would argue that this coming year will actually look a little better in terms of economic activity than this year has already," Porcelli said.