Boudjellal was quoted in several media reports earlier this week saying Armitage had asked to be released from the last year of his contract with Toulon to return to England, after being contacted by Jones.
But the England coach has now poured cold water on those claims, saying the conversation never took place.
"I don't control him (Armitage)... at the moment he is not eligible to play for England," Jones told British media.
Wasps are interested in bringing Armitage back to England, according to British media reports, but Jones said the player was not guaranteed a place in the squad even if the deal went through.
"It's not up to me, it's up to him. If he signs for Wasps, gets fit and plays good rugby I'll pick him," Jones added.
Armitage last played for his country six years ago.
Jones has selected a 26-man provisional training squad ahead of England's tour of Australia, which takes place in June.
(Reporting by Nivedita Shankar in Bengaluru; Editing by Toby Chopra)
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