England crashed out of the tournament on Saturday with a 19-12 quarter-final defeat to France at Eden Park - their worst World Cup performance since 1999.
Johnson's contract as England manager expires on December 21 and immediately after the game he said he would spend the next few days considering his options.
Martyn Thomas, who drove Johnson's appointment in 2008, told BBC Radio 5 Live: "It's a matter for him to make that decision as to whether he wants to continue into 2015. He has my backing, certainly."
Thomas' decision to open the door for Johnson to continue flies in the face of the "robust" review process announced earlier in the day by Rob Andrew.
Not for the first time in recent months, two senior RFU official are at odds with one another.
Andrew, the RFU's rugby operations director, will talk extensively with Johnson, the coaches and senior players before formulating England's plan to win the World Cup on home soil in 2015.
The management board, on which Thomas sits, will then be asked to vote on Andrew's recommendations, which may or may not include retaining Johnson as manager.
"It is my job to review the World Cup and make a recommendation to the RFU management board," Andrew said.
"In July 2008 we said we would support Martin right through to the World Cup and then reflect on what happened and go forward from there.
"Martin needs to think about it so does the RFU so we can actually move on and take things forward with this group of players.
"At some point between now and Christmas we will make our recommendation about the shape of the England management team.
"At the very, very latest from January 1, 2012 we will be in a position to pick a Six Nations squad and start the campaign through the Six Nations in 2012 and through to 2015.
"These World Cups come around quickly and you cannot afford to lose any time in terms of the management team and the players you want in that cycle."
Andrew added the RFU had learned from the way they conducted the post-World Cup review in 2007, which led to Brian Ashton being elbowed out for Johnson.
"We will do it quickly and openly," Andrew said, although he perhaps did not expect Thomas to be as open as he was today.
The RFU's top brass are in such a state of disarray that Andrew is not even sure who will be in on the management board by the time his review is concluded.
Thomas is facing a potential vote of no confidence from the grass-roots clubs for his handling of John Steele's departure as chief executive.
"There is a management board, regardless of what happens with the political dynamic over the next few weeks and months," Andrew said.
"At the point we finish the review and make a recommendation, there will be a management board to report to. Quite who will be on there..."
The political schism at Twickenham has led to a second restructure in the space of 10 months, with the RFU scrapping plans to appoint a performance director above the England coach.
Johnson has always rejected the notion that anyone above him should have a direct input into the England team.
Instead, Andrew is on the verge of accepting a contract to become the new professional rugby director - his third job title in a year.
"My position going forward will...effectively be managing director of the professional game from an RFU's point of view," Andrew said.
"What we will do over the next few months is look at the whole performance structure, the professional department of the game.
"We have a performance system that is already in place. Stuart Lancaster is filling that role in terms of player development.
"I think we've made some pretty big strides in terms of increasing the flow of quality players so that people will be ready for the England team.
"What we need to do over the next few months is make sure we have everything in place so we get it right in 2015 when we have the World Cup in England."
The England players queued up after the game yesterday to endorse Johnson's credentials as the best man to lead the squad into the 2015 World Cup.
Squad captain Lewis Moody lent his own support in his Mail on Sunday column today, writing: "English rugby needs him at the helm. I don't think there is anyone who can do what Johnno does."
Johnson said after England had won their first Six Nations title since 2003 that he found the manager's job addictive.
"You know you are alive," Johnson said today. "It has not been dull."
Johnson remained non-committal on his future but he does believe England are in a better place now, despite their World Cup disappointment, than when he took over in 2008.
"Now's not the time to think about my future. Whatever happens, the players have come a heck of a long way."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.