The RFU says it will not comment on what it terms "rumour and speculation".
A report in Friday's Times suggests Johnson's appointment could be ratified next week.
England's 2003 World Cup-winning captain has been linked with a managerial role for the past fortnight.
Meetings have taken place between Johnson and the RFU's elite rugby director Rob Andrew about an appointment that would require formal RFU management board approval.
The Times say Johnson would take up a position after this summer's two-Test tour of New Zealand. England face the All Blacks in Auckland and Christchurch on June 14 and 21.
They claim he has "agreed in principle," and it is thought Johnson would have control over selection, in addition to hiring and firing coaches.
Where that would leave head coach Brian Ashton and his assistants John Wells and Mike Ford is unclear.
Ashton, in charge since December 2006, has always wanted a manager, but someone with an administrative hands-off approach, rather than an individual directly involved in team affairs.
If Johnson is appointed and is given complete control, then Ashton could find his position untenable.
The likes of Australian Pat Howard, Johnson's fellow World Cup winner Mike Catt and his ex-Leicester colleague Austin Healey have all been linked with possible coaching roles.
Ashton is currently preparing for England's Twickenham appointment with the Barbarians on June 1, followed by the New Zealand trip.
He led England to second-placed finishes in the 2007 World Cup and this season's RBS 6 Nations Championship and has maintained a dignified silence while the Johnson saga has raged.