The prospective Oxford appointment stepped in as Everton caretaker boss earlier this season.
The Daily Mirror reports on page 46 of its printed edition on Monday that Oxford United are set to confirm the appointment of Everton Under-23s' manager David Unsworth.
Everton are said to have granted Unsworth permission to speak to the League One side over the weekend.
And according to the Daily Mirror, the 44-year-old, who stepped in as Everton caretaker boss earlier this season, will succeed Pep Clotet at the Kassam Stadium.
Could Everton's Oxford links strengthen with Unsworth appointment?
A renowned youth coach, Unsworth has had a hand in developing young Everton talents such as Tom Davies, Dominic Calvert-Lewin and Jonjoe Kenny.
And the former left-back could reunite with another of his one-time Toffees prospects, Ryan Ledson, if he is hired by Oxford.
While losing Unsworth would be a blow to Everton, whose U23s were crowned Premier League 2 winners last season, his departure could open up the possibility of a more formal partnership with the U's.
Oxford are currently 10th in League One - seven points off the play-off positions.