Unfortunately, there is no real way of predicting where the roots of your tree will have headed. Factors deciding root growth and spread are related to where the moisture and nutrients are, together with the avoidance of obstructions, or penetrating further away from an area that's frequently waterlogged, or, conversely, heading for an area that's frequently damp. If your tree is 6m high, it's likely that 3m is too close to the root area, but the only way to find out is when the excavation works start, I'm afraid. If the roots are heavily compromised during the works, you may need to remove the tree.

I would suggest that the spread of the tree above ground will give you an idea of whether the tree will interfere with the extension. Bear in mind not just the size of the tree today but how big is it going to be in another 5, 10, 15 years' time. Think of it the other way round - if you are putting building foundations 3m from the tree you will have a tree 3m from the building. That might be ok now if the tree only has a 1m spread but in a few years it could have a spread of 3m and be 15-20m high!

At 6m you are approaching the height at which you may need to declare it to your buildings insurer (in the UK) or find that you have voided the insurance if it gets blown over in a storm. even a falling branch demolishing your neighbour's greenhouse could leave you uninsured if you haven't advised your insurer that you have a large tree (I had to declare the local authority sycamore tree by my front gate before I was given insurance on my house)

I think its a straight choice between the extension and the tree - As Urbanite says you have to think well ahead not just about what its like now. Easier to get rid now than when its a lot bigger and there are much nicer little trees you could plant instead further away.