Charter would have to borrow heavily to complete an acquisition, and offering substantially more than $132.50, say $145 to $160 a share, may be beyond its ability to finance.
Comcast is reportedly considering buying all of Time Warner Cable, buying some of Time Warner Cable's cable-TV systems from Charter Communications, or doing nothing. Comcast has hired advisers to help with the analysis and has spoken with bankers.
Comcast officials had no comment Thursday. On Wednesday - and unrelated to the possible deal - the cable-TV and Internet giant announced plans for a second Center City tower that would cost $1.2 billion and open in 2017.
Charter spokesman Justin Venech said Thursday company executives were taking their buyout offer to large Time Warner Cable shareholders - typically pension funds and other institutional investors.
"We are meeting with them. We just can't tell you when and where," he said.
Because of how Charter structured its deal with cash and stock, Time Warner Cable shareholders would own 45 percent of the equity in a combined Charter/Time Warner Cable. A new company would serve 16 million cable-TV customers and its cable-TV lines would pass 43 million homes.
The stakes are getting high for everyone.
In a slide presentation released Tuesday, Charter disclosed that it first proposed a deal for Time Warner Cable in June, when the New York cable company's stock traded at $96 a share.
Takeover speculation has driven Time Warner Cable's share price - despite a dismal operating performance as it regards customer subscriber growth - to Thursday's close of $135.29 a share. If Time Warner Cable doesn't reach a deal, its share price could decline to about what it was before the merger talk. Time Warner Cable did not return a phone call.
Time Warner Cable lost 745,000 TV customers from the third quarter of 2012 to the third quarter of 2013, about 6 percent of its TV customer base, according to its corporate filings. As of the third quarter of 2013, Time Warner Cable had 11.4 million TV customers.
Over the same period, Comcast - with about double the TV subscribers - lost about 355,000 TV customers, or 1.6 percent of its subscriber base.
Time Warner Cable will need to invest in its telecommunications network to convert it to all-digital technology, which could be a substantial cost for the company or the entity that acquires its assets, industry experts said.