the Hubble and ISS are moving in different directions at different speeds, in different orbits at different heights from the surface of the Earth. So ... not possible.

Even if you were somehow miraculously able to make the journey from the Hubble to the ISS, the ISS would be traveling so fast relative to you, you'd die from impact.

This image points out their different angles of orbit:


Also,
The ISS is moving at 7.71 km/s
The Hubble is moving at 7.5 km/s

So, even if you somehow had a perfect trajectory towards the ISS,
given their varying directions of travel, you'd end up hitting the ISS at something like 200-1000 meters per second. You'd die. Plain and simple. There would be nothing left of you.

There's debate over whether a Kessler effect (chain reaction of debris destroying satellites) is even possible, but for the sake of fiction, I'll buy it. However, I can't buy George Clooney pointing and saying "Look, it's the ISS in plain sight, let's fly over to it" and then actually performing that feat and expecting the audience to have no problem with it. Everything up until flying to the ISS was believable and genuinely good cinema.