"There is zero evidence that they influenced the election," Sean Spicer told Fox News.
Mr Spicer, who was set to be President Trump's press secretary from 20 January, told CNN Mr Trump would see the intelligence report once it was completed later this week.
On Saturday, Mr Trump warned against being quick to pin the blame on Russia for the hacking of US emails.
Mr Trump said he knew "things that other people don't know" and would disclose some information on the issue on Tuesday or Wednesday. He gave no further detail.
"He's going to talk about his conclusions and where he thinks things stand," Spicer told CNN. "He's not going to reveal anything that was privileged or shared with him classified."
President Barack Obama expelled 35 Russian suspected spies and imposed sanctions on two Russian intelligence agencies last week for alleged Kremlin involvement in hacking.
That was based on reports from intelligence officials, including the CIA, who said Russian hackers had aimed to help the Republican Trump defeat Democrat Hillary Clinton in the 8 November election.
On Sunday, Mr Spicer said the White House may have disproportionately punished Russia.
Leading lawmakers from both parties have voiced alarm at the suggestion of Russian interference, whether or not it made a difference in the outcome.
Republican John McCain, chairman of the Senate Armed Services Committee, has scheduled a Thursday hearing on foreign cyber threats. The new Congress, elected on 8 November, takes office on Tuesday.
"It's baffling. President-elect Trump does not have any better information than President Obama," US Representative Eric Swalwell, a Democrat on the House Intelligence Committee, told MSNBC on Monday.
"The idea that we're jumping to conclusions before we have a final report is irresponsible," Spicer told CNN.
Calling for closer ties with Russian President Vladimir Putin, Mr Trump has repeatedly played down the hacking affair.
A Gallup Poll released on Monday showed less than half of Americans were confident in Mr Trump's ability to handle an international crisis, to use military force wisely or to prevent major scandals in his administration.
The poll said at least seven in 10 Americans were confident in Mr Obama, George W Bush and Bill Clinton in those areas before they took office.