San Lorenzo want Coloccini, but they cannot afford to buy him - given he signed a new long-term contract last year - meaning Newcastle would have to release him.
"We were always very clear and we said that it depends on the player," San Lorenzo president Matias Lammens told TyC Sports.
"We are going to offer him a good contract, he wants to come and I have hope that it can be done. We understand the people of Newcastle, it is hard to let a player like him leave.
"But Coloccini has to end his contract. We depend on the feelings of the player and on what he can negotiate in England. We can't buy his transfer in no way. He has been chosen as the best defender of the Premier League, he is an elite player.
"San Lorenzo can only point to Coloccini's feelings and not to his pocket. He has personal problems and wants to return to Argentina. We can only offer him a good contract."