Cleverley is undergoing a medical ahead of a loan with a view to a permanent move to Vicarage Road.
The 27-year-old is not in Ronald Koeman's plans at Everton.
Newcastle had been interested in taking Cleverley on loan, though the club, crucially, was not interested in signing the England international on a permanent basis.
United lost out on Ruben Loftus-Cheek earlier this week after Chelsea manager Antonio Conte said the midfielder would not be allowed to leave Stamford Bridge on loan in this month's transfer window.
More to follow