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 Six 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."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
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