Answer: Termites would not infest a healthy living tree. Mulch should be applied several inches thick in a flat layer over the root area; it should be kept several inches away from the trunk of the tree. The reason for this is to keep the trunk dry -- a constantly moist bark at ground level promotes rot and insect infestation, it also encourages roots to form above ground level. Never apply mulch like a "volcano" heaped up around the tree for this reason.
Mulching helps keep the soil evenly moist in the root area, helps keep down weeds, and covers bare soil in areas where lawn grass will not grow due to shade or surface tree roots. An organic mulch is good to use because it slowly breaks down over time and helps feed the soil.
Any wood mulch could potentially attract termites, but they will also be attracted to the moist environment under a gravel mulch as well. You should leave a bare strip of unmulched soil right at the foundation to discourage them crossing over if they ever do invade the mulch. Keeping the area around the foundation dry as a deterrent to termites is very important, as is proper construction of the foundation in the first place. It is a good idea to check your foundation periodically for signs of infestation, especially in spring when they swarm, whether or not you are using mulch.
Here is some information about preventing termite problems you may find helpful. You may need to cut and paste the complete url into your browser to make it work correctly.
I hope this helps!
Q&A Library Searching Tips