Interim head coach Lancaster is in temporary charge while Odgers, a firm of headhunters, scour the rugby world looking for suitable candidates to replace Martin Johnson on a permanent basis.
Big names like Nick Mallett, Jim Mallinder, Wayne Smith and Rassie Erasmus have all been linked with coaching roles in a new England set-up.
The Rugby Football Union would like to make an appointment before the end of the forthcoming Six Nations, which would seemingly count against Lancaster.
But acting chief executive Stephen Brown insisted that timescale is not set in stone.
Should Lancaster apply, Brown said he will neither be considered nor discarded on the basis of results alone. He has already impressed Twickenham executives with his role in the RFU's so-called "reputational damage rebuild plan".
Lancaster has set about reforming the culture of the England set-up by taking strong disciplinary action against Danny Care and naming a new-look squad for the Six Nations.
He has also helped the RFU's chief commercial director, Sophie Goldschmidt, take that message to sponsors who were concerned about the image of English rugby on and off the field after a turbulent 2011.
Brown said: "Stuart has made a fantastic impression and I'm sure if Stuart chooses to apply he will be given every consideration for that job.
"Stuart has to make the decision about whether he wants to be considered for the role. If he does then we will make sure there is time (for him to make his case).
"The door is not shut, it's open.
"All of the good things you have seen Stuart has done have made a massive impact and that is the kind of thing you want.
"It is not just about the results. Clearly that is important and the focus - but we need to build a team that is strong from a performance point of view and from a cultural point of view for the long term.
"They are key bits we need in place and Stuart is focused on those things as well. That is the admirable bit about Stuart (given he is only in temporary charge). He is not just focused on winning, he wants to get all of those things in place and you have seen the building blocks starting.
"To be frank, everything Stuart has done has made a very positive impact."
England's World Cup campaign was dogged by off-field scandal.
Land Rover also wrote to the RFU following the tournament to complain about the conduct of some players during a sponsors' day.
"We have worked on a reputational damage rebuild plan since the Rugby World Cup," Goldschmidt said.
"We know how important the (England) team is to everything we are trying to do with the profile they have and we've worked very closely with Stuart Lancaster in particular.
"He has already spoken about some of the cultural areas he is looking to change and improve and that has been tied in very closely with the commercial department in terms of what we want to represent as a brand and what our commercial partners expect from us.
"I think they were surprised by the extent of some of what happened (at the World Cup and afterwards). Clearly they want to see that we are learning from it and putting different measures in place to try to avoid similar incidents happening again.
"To have Stuart leading from the front and championing it has been fantastic. That is definitely having a discernible impact from the feedback I've been getting."
Goldschmidt said the RFU had not lost any sponsors or revenue following the World Cup and she admitted to being "pleasantly surprised" by the news of prospective new commercial partners who had been in contact.
The RFU today announced a four-year deal with Lucozade and Maximuscle.
All potential candidates for the England job will be considered by the selection panel, the so-called 153 group, to be chaired by the new RFU chief executive Ian Ritchie, who takes his post on February 27.
The 153 group, which also comprises two members of the RFU and two from Premiership Rugby, will then make its recommendation to the RFU board.
"The advert will be out there for a considerable period of time and that isn't just for Stuart, it's for everyone who wishes to apply. We've got headhunters out there speaking to potential candidates as well," Brown said.
"Stuart will have to make his own call. It is a major decision for anyone to make and that is his decision. It's not one we want to influence."
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.