I want to put a woodstove in my basement. However the build put the heat pump
3 feet from my thimble to my chimney... is it very expensive to move a heat pump unit about 10 feet into a corner

All cost associated with the material and labor are set locally since the prices vary around the country. It would be best to get 2 or 3 estimates locally and then you will know the exact price to move your unit..

I'm no A/C expert but I would also think it depends what is going to be in the way... basically if they have to run new ducts in an area where there are electrical, plumbing lines etc it's going to be more expensive.