The companies have now reached agreement on most terms of the deal, according to Reuters.
An announcement could come as soon as Monday before the opening bell, as the boards are expected to meet over the weekend, CNBC has learned.
Time Warner could be seeking more than $100 billion, The Wall Street Journal reported. That's about in line with $110 a share, reported by Bloomberg.
Sources also told CNBC that AT&T could pay well north of $90 a share for Time Warner, and speculated it could be up to $110 a share. Alan Gould, an analyst at Brean Capital, wrote in a research note that such a deal could hit the $110 to $125 a share range.
News of the possible value of the deal sent Time Warner shares surging 4.6 percent after hours.
The stock closed 8 percent higher in the regular Friday session, briefly breaking a 15-year high after a temporary trading halt earlier in the day. AT&T shares fell 3 percent in the regular session and fell 1 percent after hours.
The move would merge AT&T with the entertainment giant whose holdings include Warner Bros. and cable networks including TBS, TNT and CNN. Such a tie-up could be a blockbuster deal, as AT&T has a market capitalization of around $231 billion, and Time Warner has a market capitalization of close to $70 billion, as of Friday.
Time Warner and AT&T have declined to comment. Twenty-First Century Fox said it has no plans to bid for Time Warner.
Bloomberg initially reported Thursday that executives of both companies had discussed a possible merger. The two companies had also discussed a number of alternatives, people familiar with the matter told CNBC.
The Wall Street Journal also intially reported details of the timing of the talks. While Bloomberg reported an Apple bid is unlikely, the Journal said Apple is "monitoring the situation" and that Apple had approached Time Warner a few months ago.
Apple declined to comment. Alphabet did not immediately respond to a request for comment, but is apparently not interested in a deal. It's unclear whether a provision for other companies to "shop" would be included in the deal at this point.
Word of the imminent deal comes amid consolidation in the media industry, as more customers "cut the cord" on their cable subscriptions, providing a challenge to TV companies. For example, nearly 6 percent of subscribers told Magid Advisors they were "extremely likely" to cancel their service in the next year, from just under 2 percent in 2011.
Time Warner owns HBO, which has a popular streaming offering.
"When you think about how content is being consumed today, more and more of millennials are consuming content over tablets, over their smartphones," Amir Rozwadowski, head of telecom services research at Barclays, told CNBC's "Power Lunch" on Friday. "When you think about that opportunity set, there's a tremendous opportunity to push content to those subscribers."
Taking into account DirectTV and wireless customers, AT&T has grown to become one of the largest distributors of video content nationwide, Rozwadowski said.
"We have always believed that the combination of content and distribution makes sense and over the long term [Time Warner] has been the greatest content factory for films and TV," Gould of Brean Capital wrote.
CNBC had previously reported that AT&T wanted to buy a media company, including potentially Time Warner, as rivals such as Verizon and Comcast have made moves in the media business, with ownership of properties like AOL and NBCUniversal, respectively.
Owning a media company can be a powerful advertising play, leveraging data on telecommunications customers.
"The challenge a company like AT&T has ... is that they're landlocked to the relationships they have with consumers," Greg Portell, partner in A.T. Kearney's consumer products and retail and communications, media & technology practices, said earlier this fall. "What content gets them is economic opportunities beyond their consumer base."
But Barry Diller, chairman of IAC, told CNBC this week that Time Warner faces the challenge to figure out the course from "old media" company to thinking digitally. But AT&T's base of wireless customers may not be the answer.
"Those are huge challenges," Diller said in an interview that aired Friday on "Squawk Alley." "If you can't figure something out, you get bought. I like very much Time Warner. Its management I think are really good, and there's every reason they will figure it out. I don't think AT&T helps them."
— Reuters and CNBC's Mariam Amini, Josh Lipton and Michelle Castillo contributed to this report.
Disclosure: Comcast is the owner of NBCUniversal, the parent company of CNBC and CNBC.com. Barclay's received non-investment-banking related compensation including compensation for brokerage services, if applicable) from AT&T and/or Time Warner. Barclay's is a market-maker in debt and equity securities issued by this issuer.