Jones free to coach B&I Lions in South Africa
Jones signed a contract extension which will see him stay on as England head coach until 2021.
The Australian's original contract was due to end after the Rugby World Cup in Japan in 2019.
The new deal will also allow him to be involved with the British and Irish Lions side for their tour to South Africa if the Lions Board does approach him.
Rugby Football Union Chief Executive did not disclose whether there is a specific Lions clause in the new contract, but he also insisted it would not stop Jones from joining the combined side.
"No, it wouldn’t prohibit him at all," said Brown in an interview on the Telegraph's website.
"Bear in mind that we're a quarter-shareholder in the Lions and we'll have some say in that too. Our view in that would be that if we're planning for success, and we've come out of a very successful World Cup, and Eddie is the right coach for the Lions, the arrangement isn't going to preclude that.
"We're not ruling it out. But it's quite a way away and there are a lot of things to happen before then and it's not entirely our say either. This is fundamentally about England, but no, it doesn’t preclude a Lions situation if it were to occur."
Meanwhile, Jones said he is "not arrogant or presumptuous enough to think I would be offered the Lions role".
"It is not really part of my rugby history," he said. "I would see that as being consequential of coaching well, so it is not something I really think about or worry about."