You neglect to provide the most important info, which is how tall the
tree is. These can grow to 50-70 feet. If it's 25ft or under, it can
probably be moved by a tree service. They have trucks with a spade
type device that goes around the tree and takes it out with a ball.
Trees of that size are moved all the time for landscape applications
where they want a mature tree and are willing to pay for it, but it
ain't cheap. You can call around to some tree services and get quotes.

Of course there is risk that the tree will die, there is no guarantee.
You could also check with any local agricultural services, as they may
have experience with how hardy that variety is to that type of
transplant.

And obviously, if you're going to do this, I'd do it before the house
goes on the market, or at least tell potential buyers you are gonna
move it before closing, make sure it's in the contract, etc.