President Donald Trump is pushing hard to strike a trade deal with China in the hope of lifting the stock market ahead of his re-election bid, three sources briefed on talks told CNBC.

The sources said Trump wants a rally as he gets set to run for a second term and has decided that resolving the U.S.-China trade dispute can make that happen.

The president is increasingly concerned that the lack of a trade agreement could knock down stocks, Bloomberg News reported earlier Wednesday. Trump has taken notice of the market's gains as both sides get closer to a deal, the report added.

U.S. stocks started 2019 strong, with the surging more than 11 percent through Tuesday's close. Part of the rally has been fueled by investors increasing bets that China and the U.S. will strike a trade deal soon. However, there are growing concerns that a deal is fully baked into the market, possibly limiting any more gains coming from positive trade news.