The 60-year-old would surpass World Cup winner Clive Woodward as England's longest-serving coach if he stays in charge until the next World Cup in France.
The Rugby Football Union were expected to make an announcement later on Thursday, the report said.
England head coach Eddie Jones
Image credit: Reuters
"We have a great team and I am excited about raising the standards again," Jones said.
The timing of the announcement comes during the current coronavirus crisis, with many at the RFU and in the wider rugby community fearing for their futures, and Jones having already agreed to a pay-cut..
"My thoughts and those of all of us at the RFU are with everyone impacted by Covid-19, both across the country at large but also within our own rugby union community. In exceptionally difficult times, we are pleased to be sharing some good news," said RFU chief executive Bill Sweeney.
Jones added: "The extension is a great honour for me, but in the current environment, it is only right to acknowledge what a difficult time the world is facing. We are all looking forward to a time when we can get back to playing rugby and use the sport as a force for good in bringing people back together."