Last month Robertson confirmed his interest in the England role.
“I’ve said it many times that the All Blacks is my preferred choice but if it didn’t work out that way, you know, England’s got so much potential, it’d be a pretty special job,” Robertson told iNews.
“There is potential to any international job, I’ll make that clear, because there’s a few coming up [after the 2023 World Cup]. My first choice is to be at home. And then what other potential, if it is England, Scotland or Australia or any other team that’s out there, you’ve got to look at it.
“I’m in constant contact with the NZRU ... but you consider any opportunity in international football because there’s not many of them and it’s a four-year cycle.”
Jones guided England to a Six Nations Grand Slam in his first tournament as coach in 2016. It kicked off a run of 18 straight victories which ended the following year at the Six Nations, though England would retain the title.
England then reached the final of the 2019 World Cup in Japan, beating defending champion New Zealand in the semifinals before falling to South Africa.
Jones captured a third Six Nations in 2020 before his fortunes started to turn. A fifth-place finish in the tournament in 2021 was followed by England coming third this year.
Pressure continued to build on Jones during the recent autumn internationals as England won just one of four games and was booed off the field after a 27-13 loss to South Africa in the finale at Twickenham.
That led to a review of the England program which signalled the end for Jones.
“I am pleased with much that we have achieved as an England team and I look forward to watching the team’s performance in the future,” Jones said in a statement from the Rugby Football Union.
“Many of the players and I will no doubt keep in touch and I wish them all well in their future careers.”
RFU chief executive Bill Sweeney noted the “huge contribution” Jones made to English rugby.
“He has the highest win ratio of any previous England head coach and has helped develop the leadership skills of many players and coaches,” Sweeney said.
“I am grateful to Eddie for all he has done for England across many areas of the game and the professional way in which he has approached reviewing the performance of the team. He has provided the panel with astute insight and meaningful lessons that will support the team performance going forward.”
Forwards coach Richard Cockerill will take charge of the program on an interim basis, the RFU said.