As long as he likes. He can even lose it to the opponent and let the opponent score an easy goal. Only once he takes possession of the ball with his hands is there a time limit. He then has 6 seconds to release it back into play.
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Once the goal keeper has taken possession of the ball with his hands they have 6 seconds to release the ball back into play. The referee, in general, will not be counting and will verbally warn the goal keeper before taking action. If it continues, then play will be stopped and an indirect free kick will be awarded to the opponents at the location of the infraction.
The goalkeeper has an unlimited amount of time if it is a back pass because he is deemed to be a defender. However, if it was from a save, 6 seconds.
A goalkeeper cannot hold the ball for more than six seconds. The penalty for going over six seconds is an indirect free kick for the other team.
They're normally allowed no more than six seconds, but to honest I don't think anyone really enforces it any more...
The goal keeper has 6 seconds to release the ball. The referee will most likely give verbal warnings before penalizing the goal keeper.