In little more than three months as interim coach, Lancaster has helped transform the image of English rugby after a shambolic World Cup campaign. He has also guided his overhauled team to three away wins in the Six Nations for the first time since the competition was expanded in 2000.
Captain Chris Robshaw has already thrown his weight behind Lancaster to replace Martin Johnson.
However, Ian Ritchie, chief executive of the Rugby Football Union, will not be swayed by the clamor for Lancaster's appointment.
"Stuart has been doing a fantastic job and this was a great result [against France], it is a helpful thing to strengthen his case," Ritchie said. "We are going through a process.
"It is not going to be based on what happens in the Six Nations alone - whether we had lost to France, whether we had won or what happens against Ireland next weekend."
England can still win the northern hemisphere tournament going into the final weekend, but would need to beat Ireland at Twickenham and hope Wales slip up at home to France. A points difference of 38 in favor of Wales would also have to be overturned.
Nick Mallett, the former South Africa and Italy coach, is also believed to have applied for the post and has significantly more international experience than Lancaster.
But Lancaster, a renowned disciplinarian, has been praised for bringing a sense of pride back into playing for England.
"Is it clear as well the team performs for Stuart? It is very clear," Ritchie said. "We have the team heading in the right direction because the basic values Stuart has imbued into the team are the basic values we all agree with.
"When we are looking at the candidates who are in the frame, it is comparing different skills, different backgrounds, different experiences. It is a comparative exercise ... It is a big call and a difficult decision."
Ritchie said the RFU would not make an appointment before the end of the Six Nations.
