The allegation was made by Michael Wolff in "Fire and Fury" an excerpt of which appeared in The Guardian newspaper.
The author, a former Guardian columnist, claimed that Blair traveled to the White House in February 2017 to meet with Trump’s son-in-law and aide Jared Kushner.
He reportedly told Kushner that "the British had had the Trump campaign staff under surveillance, monitoring its telephone calls and other communications and possibly even Trump himself."
Blair explained to Kushner, Wolff wrote, that the Barack Obama administration would not have asked the British to spy on the Trump campaign [but] the Brits would have been led to understand how helpful it might be if they did.
White House Press Secretary Sarah Sanders has described the upcoming book as "trashy tabloid fiction" filled with "false and misleading" accounts from individuals who have no access or influence with the White House.