Yes it is possible to move your asparagus to a different location in your garden and it should be moved while it is still dormant to prevent shocking the roots, so in very early spring if you want to do it before summer or hold off until later in the year.

Digging up an established asparagus crown can be quite laborious but try to dig out as much of the root system as you possibly can and replant by planting in a trench that is wide enough to accommodate the root ball and covering with 4-5 inches of soil. Water the plant in its new location thoroughly.