I would expect you would have better success negotiating them to cover the costs of the move either through reimbursement or a one time flat sum payment (if this is an intracompany move, this applies even more, I would say). Generally, you are looking at them covering the cost of moving your household goods and helping you manage getting out of your living arrangements in the old place(selling house, buying out lease, etc.) and setting them up in the new place.
Their willingness to do this may vary, but I’d say you have a better shot if they are trying to get you to move within the company. I’ve not heard of a salary increase due to one-time moving costs, only cost of living increase.
Now, if you’re taking on new responsibilities, etc., that may be cause to negotiate a raise, but I don’t think you should base that on the cost of the move, either from the standpoint of figuring out how much to ask for or justifying it to the company.