A spokesman for Cambridge Analytica did not respond to requests for comment on Wednesday evening.

It is not clear precisely when the two men corresponded. CNN reported on Wednesday that the emails were exchanged in the summer of 2016. Cambridge Analytica was being paid by a rival campaign — that of Senator Ted Cruz of Texas — through early June, according to Federal Election Commission records. By early summer, Cambridge Analytica had also begun wooing the Trump campaign, which hired the firm in June. The firm’s principal owner is the conservative billionaire Robert Mercer, who backed Mr. Cruz during the campaign before switching his allegiance to Mr. Trump.

It is also unclear why Mr. Nix would have believed that Mr. Assange had copies of the missing emails. Earlier last year, WikiLeaks had posted a searchable database of more than 50,000 emails from Mrs. Clinton’s private server, all of them previously released by the State Department. But Mr. Trump himself seemed eager to find the missing emails: At a campaign rally in July, Mr. Trump publicly asked Russia to obtain the deleted emails.

“Russia, if you’re listening, I hope you’re able to find the 30,000 emails that are missing,” Mr. Trump said.

The communication with Mr. Nix could more closely link the Trump campaign and Mr. Assange, whose website has published thousands of emails stolen from Democratic officials. United States intelligence agencies believe the documents were originally obtained by Russia-linked hackers. Another Trump adviser, the political consultant Roger Stone, has disclosed that he was in touch with Mr. Assange through intermediaries; during the campaign, Mr. Stone occasionally previewed WikiLeaks releases of stolen emails from Democratic officials.

Cambridge Analytica has drawn criticism inside and outside the Republican Party, both for its claim to be able to classify voters by psychology and for exaggerating its role in Mr. Trump’s upset victory. Former Trump campaign officials have said publicly and privately over the last year that Cambridge functioned as one of several data and analytics vendors for the campaign. While the Republican National Committee provided the campaign’s core voter data, those officials said, Cambridge provided personnel to the campaign and helped develop target lists for digital advertising and online fund-raising, among other tasks.