From what I can see, the roots of that tree may have already discovered
your foundation. But, they may not do it any harm.
Here's what most people imagine a tree to be like:
They imagine the root system below ground to be similar in depth and
areal extent to the branch system above ground, and that's not true.
Here's a more realistic and conservative idea of what happens
The roots extend out to a diameter of 2 to 4 times as far as the
branches do, and 99 percent of the root system is less than 24 inches
underground with virtually all of the roots within 3 feet of the
surface. It's a conservative depiction because the root diameter could
extend twice what it's depicted to be for the size of the tree's crown.
The reason for the misconception about trees is that people think the
job of the root system is so collect moisture for the tree, and in order
for the tree to survive a drought, the roots would have to go deep into
the ground. The root system is extensive and shallow because the roots
primary job is to collect nutrients the tree needs to grow. And, the
kind of nutrients a tree needs are the result of AEROBIC decomosition of
organic matter. Basically the tree wants to eat good quality compost.
And, it's only the top 24 inches of ground that has enough oxygen in it
for aerobic decomposition to occur. Anything more than 3 feet down, and
there's not enough air in the ground for aerobic decomposition, so any
decomposition that takes place is anaerobic decomposition, and trees
don't like that kind of food.
So, in your photo, if the tree branch diameter is about a meter (I'd
say), it's reasonable to assume that the root diameter is 2 to 4 meters,
so if your house is 3 to 4 meters away, the roots from that tree are
anywhere from half way to your foundation to all the way there by now.
I'm not an arborist, so I don't know if or how the road or sidewalks
around that tree would affect it's growth or the growth of it's roots.
I would phone up your city and ask if they have an arborist on staff,
and see what he/she says about the root system and your foundation. If
you simply cut a thin trench around your house 24 inches deep, slide in
some stainless steel sheet metal and that trench in again, you should
stop any further root growth in the direction of your house. Hopefully
your city's arborist(s) will have a better game plan that's be easier or
less expensive. If your city doesn't have an arborist on staff, then
your provincial or state government certainly should.