Johnson announced today he had decided to stand down after presiding over England's disappointing World Cup campaign, which ended with a quarter-final defeat to France.
Jones insisted the rewards of getting England back on track were "enormous" with the 2015 World Cup being played on home soil.
He told BBC Radio Five Live: "You'd always be interested in coaching England.
"It has got a fantastic domestic competition, very, very good players and you have just got to get the right programme in place and they should be good enough to win the next World Cup."
Jones led the Wallabies to the 2003 World Cup final, where they were beaten by the England team captained by Martin Johnson, and he helped coach South Africa to victory four years later.
Jones said he would not be put off by the chaotic state of the Rugby Football Union's senior management.
"Over the last period of time England rugby has lost its way and you'd have to question the people in place now," Jones said.
"That is the challenge of getting it right. If you get it right, the benefits are absolutely enormous. That is the challenge of it and that is the exciting part of it.
"You've got to find the right style of play, just as (Sir Clive) Woodward did over that period (up to 2003), work with the clubs and ensure the players are in peak condition."
Mallett revealed he was approached by the RFU this week about the prospect of taking charge of England, should Johnson resign.
The former South Africa and Italy coach was immediately installed as many people's favourite to take over at Twickenham after Johnson confirmed his decision to step down.
But Mallett confirmed he had decided against taking the RFU up on their offer on Thursday night.
"I would like to lay to rest the speculation linking me to the now-vacant England rugby coaching position," Mallett said in a statement issued by his management company Prosport International.
"The RFU contacted me earlier this week to enquire about my availability for the position, should Martin Johnson resign. I had previously expressed my interest in the position publicly and was interested to hear what RFU representatives had to say.
"After mulling it over for a few days and discussing the opportunity with close friends and family, I have decided that I will not be making myself available for the position and I have disclosed this to the RFU.
"My primary concern is my family. I am happy to have returned home to South Africa after a tremendous four-year term with the Italian national team. We are settled in Cape Town and it is my wish to be able to enjoy time with my wife and kids after four years in Italy.
"I thank the RFU for making their interest known to me. The job of England coach is one of the most prestigious in world rugby and I wish them all the best in their quest for the best possible man for the job."
Mallett, who was born in England, guided the Springboks to 17 consecutive Test victories in 1997-98 and into the semi-finals of the 1999 Rugby World Cup.
After winning two French titles with Stade Francais, Mallett was interviewed for the England job in 2006 before taking charge of Italy.
Mallett said last week he would be interested if the England job became vacant - but he would have wanted to report to the RFU management board and not Rob Andrew, as elite rugby director.
Andrew was asked today whether he would be willing to step aside if that cleared the path for the RFU to appoint the best candidate for the coach's job.
The former England fly-half rounded on the journalist who posed the question and angrily insisted he would not.
"It is a complete lack of understanding of structure," Andrew said."I am not sure how many of you worked in business and how structures work, and how reporting lines work and how a multi-million pound operation actually functions in terms of reporting lines.
"Martin's unit is a self-contained unit within the elite rugby department running the England team. That is about a fifth of the responsibilities I have in running the biggest department of the union, from a financial point of view.
"If anyone wants to come and discuss all the detail of that and understand what structure is, as opposed to perception, then please come and talk to me about it.
"No (I would not step aside) because it is a complete misunderstanding of my job, which you clearly have."