|By Chris Jones|
|BBC Radio 5 live|
Both men may be in the form of their life but the Rugby Football Union's current selection policy means the France-based pair are currently ineligible to represent the national team, bar "exceptional circumstances" which were not met.
BBC Sport looks at the issue which is dividing opinion in England and beyond.
Why is there this policy?
The policy was formalised by the Rugby Football Union in 2010 and came into effect after the 2011 World Cup.
There are two main reasons for it:
- to protect the quality of the English league by ensuring the best English players play in it
- to give the RFU more control and better access to current England or potential England players.
The Welsh Rugby Union, for example, selects players who play their rugby abroad, but have had problems accessing those at clubs in France and England.
How has it impacted England?
On the whole, the policy has achieved its aim, with the vast majority of English players having opted for international honours over better wages in places like France.
But prop Andrew Sheridan in effect ended his 40-cap England career by deciding to join French side Toulon in 2012, while fly-half Toby Flood did likewise when moving to Toulouse last summer.
Back rower James Haskell put his England career on hold to play for clubs in New Zealand and Japan, but the policy didn't impact on the international career of former Toulon fly-half Jonny Wilkinson, who retired from international duty following the 2011 World Cup.
Who is in favour of it?
Clubs in the English Premiership, for a start.
"You want English players playing in the Premiership," says Leicester Tigers director of rugby Richard Cockerill. "If you take that away and allow players to go anywhere in the world and still get picked for England, then I think it would be hugely damaging to the Premiership."
Welshman Dai Young, now boss of Premiership side Wasps, agrees.
"England's stance is by far the best," he says. "They should stick to it, otherwise you will see the quality of the Premiership dwindle."
He also argues it is harder to monitor a player's fitness, condition and welfare if they move abroad.
And those against?
World-Cup winning full-back Iain Balshaw cannot understand why England do not want to be able to pick 2014 European player of the year Armitage, who plays for Toulon, and his successor Abendanon, who represents Clermont Auvergne, if they so desire.
"We have to do everything we possibly can to give ourselves the best chance of winning the World Cup," says Balshaw, who played for Biarritz for five years and still lives in France.
"It's not as though these guys - Armitage and Abendanon - are playing for mediocre teams. They are playing for the two best teams in Europe. They are training - week in, week out - with some of the best players in the world."
Former England prop David Flatman agrees that a move to France can improve a player and says the current selection policy could put the RFU into a difficult hole.
"Say, for example, you have a young loose-head prop, like Northampton's Alex Waller. He's not quite getting the nod for England. What if he goes to play for Toulon and plays with former New Zealand prop Carl Hayman and gets better and better and better? What happens then?"
What do other countries do?
After Australia recently relaxed their eligibility criteria, England and New Zealand are now the only two major nations to pick only home-based players.
Wales select players based overseas but have been heavily criticised for their stance.
With the regional teams in Wales struggling financially over the past few seasons, a number of key players, such as Jamie Roberts, Leigh Halfpenny, Jonathan Davies, George North and Dan Lydiate, have all moved abroad knowing they could continue playing for the national side.
That exodus has weakened the Welsh domestic game even further.
Interestingly, Wales head coach Warren Gatland, a New Zealander, says he wouldn't pick French-based players if he were in charge of England.
He claims he wouldn't need to given the player resources available to the English.
What if England's rule was changed?
It will be "hugely damaging", according to Leicester boss Cockerill.
"You could go out and play in Japan in the first part of the season and come and play the Six Nations in England and double your money," he says.
Flatman, on the other hand, thinks scrapping the selection policy would be a positive step for English rugby.
He certainly does not believe it would lead to a mass exodus of English players to France.
"We are flattering ourselves to think the French clubs are clamouring for English players," he says.
Interestingly, he suggests that if more English players become available on the open market, French clubs may not have to pay as much in wages because there will be more choice.
He also reckons players leaving for France would open up opportunities back home for others, like Jamie Gibson and Anthony Watson, who replaced Armitage and Abendanon at London Irish and Bath respectively.
"There are arguments both ways and pros for pretty much every con," says Flatman.