We say clocks tick slowly in the strong gravitational fields. Is this stated from the perspective view of the one located in a weaker field or the one who is standing in that strong gravitational field? In Special Relativity the time dilation of clocks is said from the view of observers constrained to the other inertial frames and no observer can judge the rate of clock ticks in his own inertial frame.
If I've understood correctly, there is by definition nothing an observer can say about the "slowness" of their own clock. Therefore all statements about an observers clock slowing down must be relative to another observer who is not in a similar situation. In this case it means that when an observer without a gravitational field observes a clock in a strong gravitational field, they find that the clock is ticking more slowly. An observer right next to the clock never sees any slow down. More informally this can be thought to be because the observer itself is also slowed down. EDIT: As it occurs in the comments, the last sentence is not a good way go thinking about things, as it would imply an observer slowing down compared to some global clock. While this can be the case in gravitation induced slowing, the mind set cannot be applied in moving inertial frames.
In general, a Schwarzschild observer, who is away from the effects of the gravitational field, deduces that time dilates for the clocks inside a G-field. Although any other observers located at distances greater from the G-mass than the clock can detect different time dilations considering their distances from the G-mass and from the clock, a Schwarzschild observer is a more formal one.