Stocks rose on Friday as investors cheered potential progress in trade negotiations between China and the U.S.

The Dow Jones Industrial Average rose 336.25 points to 24,706.35, led by gains in UnitedHealth and Home Depot. The S&P 500 climbed 1.3 percent to 2,670.71, closing out of correction territory, as the materials and industrials sectors outperformed. The Nasdaq Composite advanced 1 percent to close at 7,157.23.

The major averages jumped to their highs of the day after sources told CNBC that China had offered a six-year increase in U.S. imports during recent trade talks. Bloomberg News reported on Friday that the deal would aim to reduce the annual U.S. deficit to zero by 2024.

Shares of Boeing and Caterpillar both closed more than 1.5 percent higher. Deere climbed more than 2.5 percent.

"That's the key factor," said Randy Frederick, vice president of trading and derivatives at the Schwab Center for Financial Research. "If we don't get that issue resolved, the market is going to hit upside headwinds no matter what happens."

"If we get that issue out of the way, which will boost business and consumer confidence, there is still plenty of room for the market to do really well," said Frederick.

On Thursday, The Wall Street Journal reported that Treasury Secretary Steven Mnuchin had floated the idea of easing tariffs on Chinese goods as the two countries continue to negotiate on trade. The report sent the major indexes to their session highs on Thursday. However, a senior administration official told CNBC that there is "no discussion of lifting tariffs now."

The Dow and S&P 500 posted their fourth straight week of gains, their longest since August. They both gained more than 2 percent. Stocks are also up sharply to start the year. In fact, 13 trading days in, it's the best start to a year for the S&P 500 since 1987, according to Bespoke Group.

"What we're seeing, in terms of valuation, now that markets have recovered a lot of the lost ground, is they're starting to become overvalued once again," said Petra Bakosova, chief operating officer at Hull Tactical. "When the market bottomed out in December, that was a buying opportunity."