There were certainly people who put forward heliocentric ideas prior to Copernicus. Copernicus saw himself as a resurrector of ancient knowledge, not the creator of a new theory. Copernicus himself specifically references many Ancient Greek authors (Copernicus' approach is in many ways essentially Pythagorean) and scholars from the Muslim world, notably al-Bitruji, a Spanish-Muslim astronomer. Al-Bitruji was well-known to European astronomers in Copernicus' time; he attacked the Ptolemaic model and developed several other ways of understanding planetary motion, but was not heliocentric himself, though he did discuss the possibility of heliocentrism. Other Muslim scholars that Copernicus explicitly referenced in his book are Al-Battani and Ibn Rushd, both about planetary motions. Many Muslim scholars were critical of Ptolemy, and Copernicus seems to have found these criticisms generative.

Did prior thinkers have heliocentric models? Some did. Aristarchus of Samos was said to have argued for heliocentricity in 200 BCE or so; Copernicus was aware of this argument, but did not mention him in the published version of his book (he had a small reference to him that got removed and not re-integrated until the 19th century). Nicholas Oresme, a medieval European scholar, also discussed the possibility of heliocentrism, though ultimately concluded that he preferred the geocentric model.

To get to your main question: did the Chinese or Muslim scholars explicitly outline heliocentric theories beyond what has been mentioned? I don't find solid reference to any, though it is hardly impossible. My searching through Joseph Needham's extensive Science and Civilization in China does not turn up any examples of the Chinese thinking along these lines prior to the arrival of the Jesuits, and in general I think it is fair to say that this kind of cosmological speculation is not quite the sort of thing that the Chinese astronomers were concerned with prior to influence from Europe (their approach to astronomy was more bureaucratic/data-acquiring than theory-centric). It seems unlikely to me that, over the course of their long history of organized astronomy, nobody contemplated whether the Earth might move around the Sun, but I don't have a record of it at hand.

But I would take issue with the term "discovered" here. Did Copernicus discover that the universe was heliocentric? No. He hypothesized/theorized that it was. There is a big difference there. "Discovered" implies that some kind of decisive evidence was found — this was not the case. Copernicus' approach was based on aesthetics, not evidence. It did not provide better data than the dominant Ptolemaic model, and had many strikes against it from a physical point of view (because they did not have the physics necessary to account for questions about why, if the world is rotating rapidly on its axis and also whooshing around in space, we don't just fly off of it). It was a provocative proposal to people who shared Copernicus' aesthetic concerns, and to people (like Johannes Kepler) who were also essentially sun-worshippers in the Pythagorean mode.

Kepler's discovery of his principles of orbital dynamics is the more important "discovery" here, as it actually made a heliocentric model fit the data well for the first time, and Galileo's telescopic discovery of the phases of Venus decisively disproved the Ptolemaic model (but not the geocentric Tychonic model) — these are the "discoveries" that made heliocentrism a viable system for use.

I only bring this up because there is a game in the history of science, often regarding national or ethnic priority, that involves searching for the first instance of an idea being held, and then holding that person up as the "discoverer" of some truth we today believe is to some degree valid. This is mostly a waste of time and not insightful for the process of science or its history. Copernicus is important not because he was the first person to come up with this idea, but because there were those in the immediate generation afterwards who took up the idea further and actually made it work. Frankly Kepler ought to get more credit than Copernicus, and arguably more than even Galileo, for the success of heliocentric theory — not because he was the first person to have an idea, but because he was the person whose subsequent work on said idea actually made it viable. (That Kepler stumbled across his laws while pursuing alternative hypotheses, and still saw the work through until the end despite it disproving what he had wanted to believe, is an additional mark in his favor, as I see it.)