You shouldn't glue the heatsink/fan to the CPU. You can apply heatsink compound, or else you use the heat conducting pad that is sometimes attached to the bottom of the heatsink (on most boxed CPUs), but it's been close to ten years since I've seen/heard of anyone using glue on the CPU/fan (mainly because if the inexpensive fans dies, then the expensive CPU gets trashed with it). Are you sure that it's actually glue?
If it is just heatsink compound you can clean it off with an alcohol pad/swab, let it dry, and then re-apply it before mounting the whole thing in a new board.
Regardless, just "pushing it in" probably won't do the trick. It takes a significant amount of force to make the proper surface contact between a modern CPU and heatsink. Without that pressure holding the heatsink on, it won't cool properly. Also, if the case is a tower (or some other situation where the heatsink is on it's side), the weight of the heatsink will be pulling on the CPU, potentially causing all sorts of other problems.