Accordingly Everton, where Moyes has been working without a No2 since Alan Irvine's departure for the manager's job at Preston North End last November, are keen to finalise the Round deal this weekend.
Chelsea are believed to have given serious consideration to the idea of recruiting the 37-year-old former Middlesbrough and England coach but, with all new backroom appointments on hold until Luiz Felipe Scolari begins work as the London club's manager, Everton's move for Round appears timely.