And Woodward, who guided England to World Cup glory in 2003, believes entrepreneurial spirit could be more important to transforming red rose fortunes than experience.
Northampton director of rugby Jim Mallinder is the leading domestic candidate having guided the Saints from the second division into last season's Heineken Cup final.
Some people feel Mallinder does not yet have the required gravitas when compared with a veteran coach like Graham Henry, who has just won the World Cup with New Zealand.
Woodward told Sky Sports: "I've got nothing against foreign coaches but I'm very clear on what it takes to become the head coach of England and what skill set you need.
"You could have an inexperienced coach, as long as you interview him properly, as long he's got the skill set.
"My experience is that when people are given the chances, they can step up to the plate. There's various English coaches around who, given the chance, could actually blow you away.
"We don't have to assume a Graham Henry is the right person.
"When I was involved, one of the big things we looked for was could we get 80,000 people on their feet going nuts?
"That's what I'd ask a coach. What would you do? How are you going to get Twickenham so excited about you, your team, your selection, what you going to do?
"And unless they can convince that, then I wouldn't want to know, but I wouldn't not choose somebody because they happen not to have been an experienced coach or been through the traps.
"In many ways sometimes the old coach can become quite conservative in what they are looking for.
"I'd be looking for almost an entrepreneurial person to say 'how can we take this to a new level? Can we get Twickenham back really excited about this team?"'
RFU elite rugby director Rob Andrew will oversee the recruitment of Johnson's replacement, the fourth England head coach during his five-year tenure at Twickenham.
Woodward urged the RFU to take their time, to set up an interim England management team to take care of the Six Nations and concentrate on making the right appointment.
The next England coach will be charged with leading the team into the 2015 World Cup on home soil.
Woodward accused the RFU's top brass of letting Johnson down after they recruited him in 2008 without any managerial experience.
"We've just allowed a rookie manager to just run his own ship for three and a half years without any analysis, assessment," Woodward said.
"I think that is so so wrong and someone should really be accountable for that."