Coloccini has informed the club that he would like to leave Tyneside this month to return to his native Argentina because of personal reasons.
San Lorenzo are keen on signing Coloccini with his father currently working at the club.
Alan Pardew: "We're going to sit down next week and hopefully iron out the issues and come to a conclusion where Colo stays.
"There's obviously a problem there in his life.
"The best way to deal with it at times is be on the football pitch and play your best football, and he certainly did that last week (against Norwich City)."