England internationals would oppose the inclusion of overseas-based players for the World Cup, BBC Sport understands.
Under Rugby Football Union rules, only players playing in the domestic leagues can represent England, unless there are "exceptional circumstances".
BBC rugby correspondent Ian Robertson said current squad members he had spoken to would be "outraged" if expats were made eligible for selection.
"The players don't want outsiders to come in," he told BBC Radio 5 live.
Both have been mooted as potential inclusions in Stuart Lancaster's England squad, as the exceptional circumstances clause could apply to this summer's home World Cup.
"Strictly on merit they would be good enough to be in the England squad," Robertson said of Abendanon and Armitage, who have two and five international caps respectively.
"But the players I've spoken to are unanimous that it would disrupt the squad enormously, that they would have had a free ride, taken the big money abroad and come in for the glory of the World Cup.
"And, of course, this also would affect Stuart Lancaster and his coaching team.
"I'm certain they're of exactly the same view that they have a tight squad, they've worked together non-stop for the last three years building up to the World Cup and it would be exceptionally unusual for somebody like Lancaster to want to bring in people from outside."