Highly unlikely, why are you wanting to?

They get huge eventually so it might be as well to decide now whether it is too near the wall. But moving it might well kill it.

Be aware that the monky puzzle tree will get very big and up to 60 ft tall, this will be a problem for you in the coming years if its going over the wall, is the tree near to the house? pruninig the side branches can result in dieback and if not it will look lopsided, they really need lots of space, on a lighter note does any one know why its called the monkey puzzle tree, father-in-law always said its because monkeys cannot climb them lol ?, julien.

When young (<10 years old) they are covered, trunk and all, with extremely sharp, triangular leaves. Anyone would think that a monkey would take one look, say "Eep!!", and put its hands in its armpits! : D I don't know if reality at all resembles the legend.
To address the problem, Dave, if the trunk is more than 2.5 m from the wall, so there is little danger of the roots pushing over the wall later, I would leave it there, and plan on cutting the lower branches off so people can walk under the canopy.
One drawback to that idea: the cones of adult trees can weigh up to 7 kg. That sounds like lawsuit fodder to me.
If the tree is too close to the wall, you will probably need professional help and power equipment to move it, and that is probably best done in the fall.