Citing law enforcement and other U.S. officials the Post reported that the warrant for Page was obtained last summer by the Federal Bureau of Investigation and the Justice Department from the Foreign Intelligence Surveillance Court. (wapo.st/2p3L6xi)
The judge was convinced there was probable cause to believe Page was acting as an agent of Russia, the Post said.
Page has denied in media interviews that he worked with the Russians to influence the election.
In a statement to Reuters on Tuesday, Page said the court order was evidence that the administration of former President Barack Obama wanted to "suppress dissidents" who opposed its foreign policy.
"It will be interesting to see what comes out when the unjustified basis for those FISA requests are more fully disclosed over time ...," he said.
The Justice Department did not immediately respond to requests for comment from Reuters, which could not independently confirm the Post story. The White House and FBI declined to comment.
The FBI and congressional committees are investigating whether Russia tried to influence the election in Trump's favor, mostly by hacking Democratic operatives' emails and releasing embarrassing information, or possibly by colluding with Trump associates.
Russia denies the allegations, which Trump also dismisses.