Jones is currently preparing for this year's World Cup in Japan, having taken over as England boss following England's embarrassing first-round exit on home soil at the 2015 edition.
His original plan was to step down after this year's World Cup but, in a bid to aid succession planning, the RFU announced in January 2018 the experienced Australian's deal had been extended by a further two years.
There is a reported break clause, however, in the contract which could enable former Australia and Japan coach Jones to part company with the RFU should England fail to reach the World Cup semi-finals.
But new RFU chief executive Bill Sweeney said it was now possible Jones might even stay on as Red Rose boss beyond 2021.
"Eddie has reconfirmed his commitment through to 2021," Sweeney told reporters at Twickenham on Thursday.
"So from that perspective we've already started conversations around what will the structure and look of that coaching team be coming back from Japan," he added.Sweeney's comments came as the RFU announced England assistant coach John Mitchell had signed a new two-year contract.
It means the defence specialist, a former head coach of the All Blacks, who joined England's set-up in 2018 will also see his deal running alongside that of Jones.
"We have extended John Mitchell's contract through to be consistent with Eddie's, so it goes through to June of 2021," said Sweeney.
"It is part of Eddie's long-term coaching structure plans," he added.
Wales boss Warren Gatland, who will take charge of his third successive British and Irish Lions tour in 2021, has "categorically" ruled himself out of becoming England coach in the future despite persistent speculation linking the New Zealander with a move to Twickenham.
Sweeney, a former British Olympic Association chief executive, joined the RFU in a bid to reverse financial problems that led to job cuts and the eventual departure of Twickenham predecessor Steve Brown.
But Sweeney insisted: "There's no financial crisis here."