First News Article: Heat Street
Heat Street reported that the FBI sought a warrant from the Foreign Intelligence Surveillance Court to investigate Russia's interference in the U.S. Presidential election.
Heat Street, Nov. 7, 2016: The first request, which, sources say, named Trump, was denied back in June, but the second was drawn more narrowly and was granted in October after evidence was presented of a server, possibly related to the Trump campaign, and its alleged links to two banks; SVB Bank and Russia’s Alfa Bank.
One of the authors of this article has made a public declaration that they did not report on any wiretap in the article.
Second News Article: BBC
A report from Jan. 12, 2017 from BBC, cited anonymous sources who said that the FBI received a FISA court warrant in October.
BBC, Jan. 12, 2017: On 15 October, the US secret intelligence court issued a warrant to investigate two Russian banks. This news was given to me by several sources and corroborated by someone I will identify only as a senior member of the US intelligence community. He would never volunteer anything – giving up classified information would be illegal – but he would confirm or deny what I had heard from other sources. …
Neither Mr Trump nor his associates are named in the Fisa order, which would only cover foreign citizens or foreign entities – in this case the Russian banks. But ultimately, the investigation is looking for transfers of money from Russia to the United States, each one, if proved, a felony offence.
Again, neither of the two stories support Trump's claim that President Obama ordered a wiretap.
According to Factcheck.org, the other three articles the White House provided are described as follows:
An opinion column in the conservative National Review, dated Jan. 11, 2017, that rehashed the Heat Street report and questioned if FISA was being used against “political enemies.”
A New York Times story on steps taken by the Obama administration that would allow the National Security Agency “to share globally intercepted personal communications with the government’s 16 other intelligence agencies before applying privacy protections.” This story, which ran Jan. 12, has nothing to do with the alleged wiretapping of Trump Tower, but rather how intelligence material is shared.
A New York Times story that said “law enforcement and intelligence agencies are examining intercepted communications and financial transactions as part of a broad investigation into possible links between Russian officials and associates of President-elect Donald J. Trump.” In its Jan. 19 article, the paper wrote that it “was not clear whether the intercepted communications had anything to do with Mr. Trump’s campaign.”