Charles Schwab is in talks to buy TD Ameritrade, a source told CNBC's Becky Quick on Thursday.

A deal between Schwab and TD Ameritrade would create a behemoth with more than $5 trillion in combined assets, about $3.8 trillion from Schwab and $1.3 trillion from TD Ameritrade.

"This would create a Goliath in Wealth Management," Wells Fargo senior analyst Mike Mayo said in a note to clients on Thursday.

Shares of TD Ameritrade soared 16.9% on Thursday, its best day since September 2008. Schwab's shares surged 7.3%, its best day since November 2011.

Schwab will pay $25 billion for TD Ameritrade, the Financial Times reported Thursday.

A deal between Schwab and TD Ameritrade would consolidate an industry going through massive disruption. In recent months, all of the major brokerages have announced plans to go to zero commissions. Schwab was the first of the major players to make the move, eliminating commissions in early October. Schwab's competitors, including Fidelity and TD Ameritrade, were quick to follow.

Schwab CEO Walter Bettinger has been designated to run the combined company, sources said. TD Ameritrade CEO and President Tim Hockey said in July he is leaving the brokerage in February of 2020.

Schwab's founder and Chairman Charles Schwab told CNBC's Bob Pisani last month that consolidation in the retail brokerage industry is a "logical conclusion that will occur."

"Certainty at the right valuation, we would do it, but we are really strong and very independent the way we do things, and so if its happens that it's appropriate for our shareholders we will do it," Schwab said in response to a question about whether Schwab is a possible buyer of another brokerage.

Calls to Schwab and TD Ameritrade weren't immediately returned.