How close to a very large tree can I put in a foundation for a garage

wouldn't your local council be the best people to advise you of this - I assume they will have to sign off on the build. The problem with the tree is not what you see above ground but what is below - the root system. You may find in a few years your floor cracking or worse still in a storm the tree may topple over and landing on your garage.

I would not put it near any building, like others have mentioned, you will never know where roots will grow. If they get under pad it will eventually crack. I would cut tree down and have roots cut out first, before I would ever build.