Is it common to express interest in post-doc positions well before you are qualified to apply? I'm very early in my PhD (just past 6 months) and out of interest I was looking at some post-doc positions that I could aim towards.

I found a recently advertised position that is in the exact field I am aiming for. Essentially it sounds like I'd be a perfect match... in three years time.

I was thinking of sending one of the Chief Investigators an email introducing myself and expressing interest in positions like this one for the future (obviously not applying though) so he would be aware of my name and perhaps keep me in mind so I could apply if a similar position came available at a more appropriate time.

Is this a common thing to do? Would it be positively or negatively received?

For reference, the field is mathematical biology.
One semester into your PhD is probably a little too early to start contacting potential post doc advisors and future employers—the crystal ball is way too fuzzy, and their plans almost certainly aren’t known. (They may not even be doing the same area four or five years from now!)

You could certainly contact them about your interest in your research and introduce yourself, but I would wait until you’re slightly further along to start discussing future jobs; I’d say serious discussions about that are appropriate when you’re about two years out from graduation.