While sending a space probe to orbit around a gas giant is often heard of, are there plans to send a space telescope to orbit around gas giants, so that it can operate far away from the sun, or even see the outer solar system clearer?
No, Jupiter is simply too far away (Distance = less data transmitted), it's a hard environment (Lots of radiation), and relatively little is accomplished by sending it out so far. But I do know of at least one serious proposal to send a telescope to Mars. A bare bones spy satellite (Telescope only really) was donated to NASA, and a proposal called Mars Orbiting Space Telescope (MOST). The idea is to send the telescope to Mars, where it could take photos of Mars, and take photos of deep space. It was tossed around almost 3 years ago, no idea what the current status is of it, but it seems likely it isn't going anywhere. A complete study of what might be done can be found at the Planetary Society.
There are two advantages of a telescope at Mars. The first is that it could get high resolution pictures of Mars. The second is that it would give a wider baseline, allowing us to determine where an object is with much higher precision than we can today, both inside and outside of the Solar System. I would imagine that we could extend the parallax distance from 1000 parsecs to perhaps 2000 or more. It would not be particularly useful for looking at dim objects, to keep the costs down, but would be great for looking at the gas giants, for instance.
If you're going to send a telescope far away, you shouldn't put it in orbit around a planet.
When a telescope orbits a planet, the planet blocks part of the sky, limiting your observations. It also reflects light, limiting your observations some more. In most orbits, the telescope travels through the planet's shadow cone, which leads to temperature swings.
So these days, space telescopes are sent to Lagrange points instead (the James Webb telescope will be parked at the Earth-Sun L2 point, for example).