Twitter's underwriters plan to price its stock above estimates at $27 per share as long as the market momentum Wednesday continues, sources tell CNBC.
(Read more: Opening price for Twitter keeps on going higher )
The estimated price range was originally $23-$25 per share. However, the range increased to $27 per share, indicates demand is strong.
Twitter's management will decide on the final price at the end of the day phone call.
Rett Wallace, Triton Research CEO, said he also heard whispers the company's share price would be pushed higher, as well.
"There was pushing and shoving going on today at the top end of the range, which was $25, and then that it might break north of that," Wallace said on CNBC Wednesday. "So that is consistent."
(Read more: A warning for Twitter from the first social network )
Goldman Sachs is the lead underwriter for the IPO, alongside JPMorgan Chase and Morgan Stanley. Twitter is expected to begin trading on Thursday.
The social media company is going public during a week that has 16 scheduled IPOs, which is the most offerings in a week since 2006, according to Renaissance Capital. And while investors are pleased the IPO market seems to be back in full swing, there is still some concern that Twitter's IPO could turn out like Facebook's offering, which was plagued by technical glitches and aggressive pricing.
Twitter, though, seems to be going out of its way to avoid such a repeat.
For starters, the microblogging site is listing its stock on the New York Stock Exchange, not the Nasdaq. But more importantly, Twitter's IPO is much smaller.
Facebook priced at $38 per share with a $104 billion valuation, while Twitter's estimated range was $23 to $25 per share with a $13 billion valuation.
—CNBC's Kate Kelly contributed to this report.