England to replace Jones with a Kiwi coach?
The RFU confirmed their recruitment process to identify Jones' successor is already underway.
Jones' current contract runs through until 2021, but the Telegraph report it will be terminated if England underperforms at next year's Rugby World Cup.
The RFU will consider head coaches with proven success on the international stage making Kiwis Gatland and Schmidt strong contenders for the position. The current contracts of both Schmidt and Gatland expire after the World Cup.
Gatland was at the helm of the British and Irish Lions for their closely fought series against the All Blacks last year after leading Wales to three Six Nations titles and two Grand Slams, while Schmidt completed a Grand Slam with Ireland this season.
When asked if there was an agreement in place to stay away from rival union coaches, RFU Chief Executive Steve Brown said, "No, that doesn't exist. Half of the tier-one coaches changed at the last World Cup and most of them were Northern Hemisphere, so they are going to go in different directions.
"It's pretty competitive, so no one's off limits. It's all to do with whether they fit the profile and the criteria that we're looking for. Whilst we would love to have an English head coach eventually, our priority is still to get the best coach for England."
When asked if someone like Gatland would come under consideration, Brown said: "We're not precluding anyone from the list.
"But what we're not going to do is to upset another union. We are going to be respectful of those arrangements, as we would expect others to do with us."