The reports surfaced late Tuesday, and were denied by Trump as "fake news." In tweets Wednesday morning, Trump said he has nothing to do with Russia including no deals or loans. The Russian government also issued a denial, dismissing the claims as a "total hoax."
But markets have another agenda for the 11 a.m. press briefing. Besides reassurance about the topics that have been making headlines, traders are looking for details about Trump's corporate tax plans and fiscal spending.
"The big ones are Russia and conflicts of interest," said Greg Valliere, chief global strategist at Horizon Investments, of what is likely to be discussed. "Number one is going to be conflicts of interest. There's so many juicy issues with his business ties and his kids. There will be lots of questions on conflicts and then Russia. Three would be Obamacare."
But the markets are hoping for some concrete views from Trump on policy and a checklist of his priorities. Some of the enthusiasm for the "Trump trade" has faded and bond yields have retreated from their highs, as investors await more information on the promised policies that had driven the Dow up about 9 percent since Election Day.
Michael O'Rourke, chief market strategist at JonesTrading, said Trump could create stock market volatility around the briefing, his first news conference since the election.
"There's not much of what he's saying, in my mind, that looks like it's going to shape policy or be really meaningful. I think the market has priced in a lot of optimism related to his platform and what he wants to achieve. He's not president yet, so we're still ahead of ourselves. There's so much execution risk. We'll have to see," said O'Rourke.
Stocks futures were mixed to higher Wednesday. Stocks ended Tuesday with major indexes diverging. The Dow down was 31 at 19,855; the Nasdaq was at a new record high, up 20 at 5,551, and the came in dead flat. The S&P was unchanged for the first time in nine years, closing at 2,268.90, but it did come near its all-time high during the session.
"He's a wild card. Anything he could say could create volatility," said O'Rourke. "I would argue that the bottom line is he should lead to more volatility in this market, more risk, because you don't know what he's going to say or how he's going to influence things. Right now, the market is choosing to listen to the positive side of things."
Valliere said there are differences in how Trump and Congress approach tax reform, though that's not likely to be a highlight of the news conference. Much of the market focus has been on corporate tax reforms, since that could provide the biggest bang for the economy.
"I think there's a fundamental difference on corporate taxes. On taxes in general, Trump wants big tax cuts, more generous than House Republicans. On the other hand, House Republicans are more interested in tax reform. The latter wouldn't cost as much," said Valliere.
Valliere said he would like Trump to speak about his views on the Federal Reserve, but it's also doubtful that topic will come up. He expects Congress to move on a bill to force the Fed to be more transparent, and he believes Trump would sign it if it passes. Fed officials oppose and Valliere said the market's concern is that it could politicize the Fed.
He said Trump may be asked about the fact that he tweets his views constantly.
"Trump totally lacks self-discipline, going after Meryl Streep," said Valliere, adding the president-elect also called Democratic Sen. Chuck Schumer the "head clown" in a tweet. "It's different a week from Friday. He becomes president and he can't tweet like a little kid."
Valliere pointed to the latest Quinnipiac University poll, which shows only a 37 percent approval rating on the job he's done in the transition. "He's going to have to be careful. This town is about your political capital. He's squandering his political capital with these tweets." The poll also showed that 64 percent want him to give up his Twitter account once he's in the White House.
Trump will certainly be asked about how he plans to separate himself from the Trump Organization once he's in the White House, as well as the role of his son-in-law Jared Kushner and daughter Ivanka Trump. Trump has said his sons Eric and Donald will run the Trump businesses while he is president.
On Russia, Trump had initially criticized U.S. intelligence findings that Russia hacked Democratic National Committee emails and tried to sway the election. Trump said after a briefing late last week that there was no impact on the election outcome and that he would put a team together to deal with cyberattacks by Russia, China and others.
As for Obamacare, Trump also has also said he would like Congress to repeal and replace it "very quickly or simultaneously," according to The New York Times. The Times noted that it is likely impossible, because GOP leaders are not close to coming up with a replacement for the Affordable Care Act.
As for other market events, traders will be watching the release of mortgage applications at 7 a.m. ET. There is a 10-year note auction at 1 p.m. ET, and the Department of Energy releases oil and gasoline inventory data at 10:30 a.m. ET.
O'Rourke said he is watching oil's reaction to that point, since crude futures have slid back to the level they were at when OPEC announced its deal to cut production. West Texas Intermediate crude futures settled at $50.82 per barrel Tuesday, a one-month low.