Schmidt coached Ireland to the Grand Slam this season and Gatland masterminded the British and Irish Lions drawn series against the All Blacks last year and has coached Wales to three Six Nations titles including two Grand Slams.
Asked if there was a gentleman's agreement in place to not go after rival Home Union coaches, 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.
"To be honest, 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.
"The list is long at the moment and we are looking at everybody.
"Something we are looking at is that key international experience and success is going to be pretty critical in this. Whilst we would love to have an English head coach eventually our priority is still to get the best coach for England whether they are English or not."
When asked if someone like Gatland, who also guided the Lions to a Test series victory over Australia in 2013, would come under consideration, Brown said: "We're not precluding anyone from the list, and we don't have any agreements to do that.
"But what we're not going to do (either) is to upset another Union. We are going to be respectful of those arrangements, as we would expect others to do with us."
Interestingly Brown said the RFU are also putting a plan together to increase the chances of an English coach who is in an international set-up but not the head coach job of succeeding Jones.
Brown said that if Jones, who is heavily involved in the succession plan, remains in place for two years after the World Cup, his successor could be sent on a sabbatical for two years with a Tier Two country like Georgia to gain international head coach experience.
That would bring Andy Farrell, who was appointed as Ireland's defence coach within three weeks of losing his job with England in December 2015, into strong consideration.
Farrell, who also has coaching experience with the Lions on the 2013 and 2017 tours, has played a key role in Ireland's rise to second in the World Rugby rankings. Jones' assistants such as Paul Gustard and Steve Borthwick would also come under consideration.
"One of the things we are looking at as part of the succession plan is if we select someone we would support them getting that international exposure," Brown added.
Meanwhile Brown confirmed that the RFU are considering the introduction of alcohol-free zones at Twickenham after announcing a new ticket plan that increases the access for children to attend top-flight Test matches.
