The 19-year-old striker was offered a new contract by the Pilgrims this summer but has not signed it.
Bolton Wanderers have shown interest in adding Battle to their development squad.
However, there are ongoing financial issues at the Championship club because of a player pay dispute.
So Battle is without a club less than three weeks before the start of the new season.
Argyle manager Derek Adams told Plymouth Live: “He turned down a contract with the football club so that is as far as it has gone.
“There is nothing else to add because he has turned it down.”
Battle made his debut for Argyle in the final game of last season as a late substitute in the 5-2 defeat away to Gillingham.
That came after he played regularly for the Pilgrims in the South West Peninsula League and Central League.
If Battle was to sign another for club Argyle would be entitled to a fee for him because of his age and time spent with them.
Adams said: “We are obviously due compensation because he has been with us for so many years.
“We either come to an agreement with another club or we hold out for the compensation we are due.
“There are many aspects we can go into but we do things the proper way because we have offered him a contract to stay for next season.”
Battle played as a substitute for Bolton’s under-23s side in a game against Crewe Alexandra in February.
Adams said: “Bolton are in a situation where I don’t think they can sign any players at this moment in time.”
[You must be registered and logged in to see this link.]