I assume that you mean that you want to move a variable from the part to the assembly while retaining all links to said variable.
I don't think that you can (although there might be some enterprising person who can come up with a way).
The one thing that you CAN do is to export the variable from the part to a txt file. This will make variable driven by the txt file.
Then import the txt file into all your other parts/assemblies to use as well.
yeap, thank you Dan!