Armitage is to receive the prestigious Midi Olympique 'Oscar' for the best overseas player in the French Top 14.
But he does not feature in Stuart Lancaster's plans because he would not be available for England training camps or Test matches outside of the international window.
Armitage would not be available, for example, to play for England against New Zealand on December 1 without special dispensation from Toulon.
The debate over England's need for a scavenging openside flanker in Armitage's mould intensified after Australia's Michael Hooper and South Africa's Francois Louw both turned in man-of-the-match performances at the weekend.
"I am always hoping and I will keep hoping in the future that I do get another chance with England," said Armitage.
"I hope there is a possibility there can be some negotiation (between England and Toulon) further down the line.
"I will do anything to play again for England. At the moment Toulon's where everything lies."
Asked if he would like England to try to come to arrangement with Toulon, Armitage added: "100 per cent yes. It is a big honour to put on the red rose."
Armitage won the last of his five caps off the bench against Italy in 2010. He had fallen out of favour with England's coach Martin Johnson when he moved from London Irish to Toulon 18 months ago.
Armitage felt he had gone stale after 150 games for the Exiles. He needed to kick-start his career, to recapture the hunger that first propelled him into the England set-up.
The move to the south of France, near where he played his schoolboy rugby with Nice, has done that.
Armitage has been a shining light in a star-studded Toulon squad, to such an extent that team team-mate Jonny Wilkinson has been championing his England credentials.
"If Jonny reckons I should be (in the England team) then it makes me push even harder because I don't want to let Jonny down. Jonny is one of my heroes," Armitage said.
"I knew what the risk was coming to France but I thought it would help my career more. I thought I needed that extra boost, to get back that feeling of always wanting more.
"I didn't think I could get that from staying at Irish.
"I knew it was going to be quite tough to come in and secure a starting place week in and week out.
"Toulon have players like Joe Van Niekerk and Juan Martin Fernandez Lobbe, a lot of international players.
"I knew it was going to be hard but maybe because of them I am playing better.
"I have matured a lot in the game. In the past I didn't always make the right decisions on the pitch. I am learning to be in the right place at the right time."
Armitage is strong ball-carrier but his competitive instincts at the breakdown are different to those of anyone else in the current England senior squad.
"I like getting my hands on the ball and getting my head stuck into rucks," Armitage said.
The captain Chris Robshaw is England's current number seven and he excelled at the breakdown against South Africa on the summer tour but many see him more as a blindside flanker.
Andy Saull and Worcester's Matt Kvesic are also on Lancaster's radar, although the former struggles for regular rugby with Saracens.
The England management have raised questions about Armitage's fitness but the 27-year-old insists he has never been in better shape.
"If you want to keep your place at Toulon you have to be at the top fitness-wise," Armitage said.
"I play nearly 80 minutes week in and week out in the Top 14. I feel like I am at the point where this is the fittest I have been in my whole career.
"And I am still trying to improve. You can never be fit enough."
Armitage collects the prestigious award tonight for his Toulon performances last season, his debut season in the Top 14.
"It's incredible. It still hasn't really sunk in. Looking at all the players you get in the Top 14, world-class players from all over the world. To even be nominated was a great honour."
Armitage has one more season after this on his Toulon contract and so the next 18 months will hold some important discussions, in which England is sure to feature heavily.
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