Create an object and every tick, set it to mouse.x-50 mouse.y-50 position (or touch position).
This will act as the position your object will follow, to the left and above the mouse.
When mouse is down, set the object you wish to move to the position of the object you just created. Have the object initial state to invisible.
Basically, create a new object that is offset from the mouse, by the distance you want. Then have your object follow this, instead of the mouse, or touch in your case.
Hope it helps.