ER2015, the delivery organisation for the 2015 World Cup, need to sell 2.8million tickets and a thriving England team is key to their chances of staging a successful tournament.
Lancaster was interviewed for the job on Thursday having rebuilt the England team on the pitch and restored their reputation off it during a successful interim spell.
Mallett, the former South Africa and Italy coach, would bring World Cup coaching experience and was also reportedly due to meet with the Rugby Football Union on Thursday.
"We have all seen in the last few months the improvement in the England team in the way in which they have behaved and their attitude," said Vaughan.
"The rugby public have taken to the England team. It is not for me to decide who the coach is going to be; as long as that attitude and interest is maintained in the England team I don't mind who it is.
"The demand and focus on rugby is enhanced hugely by England being successful.
"When we get our ticket strategy sorted, we very much hope to be sold out well before the tournament starts.
"The key for us is to make sure the game is in a very good place prior to the tournament, and inevitably we want it then to continue.
"A successful team means more focus on the game and that means you sell more tickets."
The World Cup in New Zealand was a roaring financial success, the International Rugby Board (IRB) announced on Thuesday, but for England it was a nightmare.
Martin Johnson's team crashed out in the quarter-finals after a campaign dogged by controversy and it later emerged the squad had been riven by a lack of trust and competing agendas.
As the squad exited Heathrow Airport via a back door, any hope that the England team could help sell their own World Cup appeared distant in the extreme.
But Lancaster led a new-look side to four wins from five matches and World Cup winner Lawrence Dallaglio is confident they are on the right track to deliver success on home soil
"In a short turnaround there is a much better feeling in and around the national team, not just on the pitch with the results but off the pitch," said Dallaglio, who is an ambassador for England Rugby 2015.
"No-one is suggesting England are the number one team in the world at the moment but they are certainly heading in the right direction."
The final World Cup venues will be decided once the IRB confirm the tournament's starting date.
It is currently slated to kick-off on September 4, but the major southern hemisphere nations want it delayed by a fortnight. The issue will be discussed at a meeting in May.
Twickenham will host the 2015 final and it is miles away - both literally and figuratively - from where the build-up to the tournament begins on Saturday as Mexico tackle Jamaica in the first match of qualifying.
Dallaglio is flying to Mexico City with the Webb Ellis Trophy to hand over the jerseys in a special pre-match ceremony and the game will be refereed by Craig Joubert, who was in charge of the 2011 World Cup final.
"The whole journey starts this weekend with the first qualifying game and it is a chance for Mexico and Jamaica to really feel part of the whole tournament," Dallaglio said.
"It should be a lively atmosphere. While these teams won't be in the World Cup finals, they have an opportunity to be in a massive game."