The Argentina striker is recovering from collapsing on the pitch last month with a heart condition. Doctors have recommended he stay away from the training pitch until January.
Goal says there has been discussion amongst Barca directors about offering Aguero a payoff from his contract and encouraging him to retire.
However, other board members are insisting management not act too soon and give the former Manchester City striker as much he needs to recover.
For his part, Aguero has stated publicly on social media he has no plans to hang up the boots.