The Rugby Football Union have advertised the position and have recruited head-hunters Odgers to scour the world for potential candidates.
Nick Mallett, Wayne Smith and Vernon Cooper are among the international names to have been linked with a role in the new England management team.
Northampton's director of rugby Jim Mallinder has been seen as the leading domestic candidate.
Lancaster, the former Leeds director of rugby, has impressed RFU executives since taking over in a caretaker capacity for the RBS 6 Nations. The deadline for applications is February 15, which is just two matches into England's title defence.
"I will be applying," Lancaster said.
"The job has been advertised. It's a good job and I am sure there will be a lot of interest worldwide and in England.
"My hat will be in the ring. I love working with teams and trying to help players improve. The opportunity to do that at the highest level with England is fantastic."Lancaster was appointed in a caretaker capacity after Martin Johnson stood down in the wake of England's failed World Cup campaign.
The closing date for applications falls four days after England face Italy in Rome and the RFU would like to make an appointment before the end of the Six Nations.
That timescale would appear to work against Lancaster, but the RFU's acting chief executive Stephen Brown has already indicated the process could be extended to accomodate his application.
Lancaster's role in the RFU's so-called "reputational damage rebuild plan" - working to change the culture of the England team and keeping concerned sponsors on board - has impressed Twickenham executives.
"I haven't applied yet but I will be before the 15th (of February). Applying is one thing, it is the end point that is the defining factor. I will send in my CV when I get the chance," Lancaster said.
"I knew when I took the job that it was an interim appointment and also knew that there was going to be a process to appoint a permanent head coach so it is not something I haven't expected.
"I don't know the timelines beyond the 15th, we will just have to wait and see what happens after that.
"The priority for me is not about Stuart Lancaster and his individual position but about getting the team together, get a team cohesive and get the team to want to play hard together and represent the country well."
Sir Clive Woodward, England's World Cup-winning coach in 2003, has described Lancaster as "lucky" to be in the caretaker job because of hs limited top-flight coaching experience.
Woodward suggested Lancaster's efforts at reforming the culture of the England squad was "good media work" but added: "In the end he will be judged solely on results. The Six Nations is a tough competition and he's got a lot to prove."
Lancaster, who spent two years as Leeds director of rugby before moving to the RFU, hit back at Woodward, insisting he does have the experience and vision required to be England coach.
"There's a lot of people giving me advice. Fortunately, I'm confident in my own coaching philosophy to believe in the way I think things should be done," Lancaster said.
"Everyone is entitled to their opinion but the opinions that really matter to me are those of the players, the leadership group, the management team and the people that surround the team.
"We want to be known as a humble, hard-working, honest team who graft and get on with the job and represent England with pride.
"The power of the nation behind you is a terrific force and we want to make sure the spectators feel excited about coming to watch and feel connected to us."
Lancaster also played down comments from Scotland coach Andy Robinson that England had behaved arrogantly during their World Cup pool clash in Auckland last October.
Robinson said Scotland would be drawing on those memories ahead of the Calcutta Cup clash with England at Murrayfield on February 4.
"I would be disappointed if, in six to 12 months time, people are saying that about us," Lancaster said.
"I can't comment about what people have said in the past or what people's perceptions were, but this is a new team and any team I have coached, I would be disappointed if people termed us as arrogant."
Lancaster will not explicity ban elaborate try celebrations, such as Chris Ashton's swallow dive, but he warned that ego-driven behaviour would not be tolerated.
"There is an energy equation in every team," Lancaster said.
"There are things that give energy to a team, such as doing selfless things, and there are thigs that take energy away - irresponsible things and ego things that are about you and not the team.
"Do you ban try celebrations, whether it is Chris Ashton or Tom Wood? No, because sometimes in the moment it is the right thing to do.
"But if I find there is behaviour that is ego-driven then I will be disappointed."
Lancaster spent 15 minutes with each player on Monday but slightly longer with Ashton, who has been at the centre of a high-profile move from Northampton to Saracens.
"I think he is a great player and in the camp he has been fantastic. He has been enthusiastic and positive, is desperate to do well and desperate to be in the team," Lancaster said.