Yes and no. Most of China's exploration was centered either in the 'Western Regions' in Central Asia or in India. Something really important to remember is that before the later dynasties, the official Chinese "empires" only controlled segments of what is modern day China, so much of their exploration was either west over the Tibetan highlands or skirting the coast to India, Southeast Asia, and, yes, even the Arabian Peninsula.
However! We do have records of Chinese explorers skirting the coasts of Africa, stopping in Ethiopia, Egypt, Iraq, and even Morocco as even farther back as the Song Dynasty (Bowman 104-105).
One notable work by Jia Dan, a military official, Route between Guangzhou and the Barbarian Sea was lost, but we do know that it included details on sea routes to East Africa and the minarets of the Persian Gulf.
A few other explorers described ivory, slave, and whale hunting in Africa. (Levathes 38). Guangzhou, in later centuries, became arguably the most diverse city in the world.
However, by the 1500s, China had receded back behind its borders, with it actually becoming a capital offense to build large ocean going ships.
##Sources
Bowman, John S. (2000). Columbia Chronologies of Asian History and Culture. New York: Columbia University Press
Levathes (1994). When China Ruled the Seas. New York: Simon & Schuster. ISBN 0-671-70158-4.
Though this is not directly addressing the cases of Chinese explorers, I think the trade relationships China had through the Silk Road are probably a lot more descriptive (and go much further back than the the cusp of the late 1500s) about how the Chinese viewed the world around them and how the Chinese viewed foreigners.
There are plenty of texts going as far back as the Tang Dynasty and the Song Dynasty due to the interactions between Middle Eastern Merchants and Chinese Merchants on the Silk Road. Though there isn't much that I've read that describes Europeans (though I am certain there are plenty) I'll focus on Middle Eastern Merchants in Tang and in Song as the most immediate material I have regards that particular time period.
So the first thing to note is the method of characterization of people and how societal norms color descriptions. In the case of the Tang, foreigners from the Xiongnu, Uighurs, to the Turks were all compared to beasts and animals with unkempt hair and poor manners. Societal comparisons are made with foreigners between Tang where culture is a result of upbringing and that manners or an understanding of Tang culture equated to a level of sophistication.
So there are clearly undertones of Sino-centrism even within the very cosmopolitian nature of the Tang Dynasty where trading cities near the Silk Road had quarters for Iranian Merchants who were described as people with "Deep eyes and high noses".
This isn't necessarily to say that the Tang saw foreigners as barbaric as much as non-native culture was seen as inferior. In fact far from it being an appearance matter, there are writings that compliment foreign merchants who acted within accord to Tang cultural norms who the Tang considered "Han" and "Han looking" Tang who were not considered Tang due to the lack of cultural fittings. Probably one of the more interesting tidbits about this exchange was the continued interest of both the Tang and the Song in the happenings of Europe. Though there was no immediacy, the turmoil in the 1200s with Constantinople and continued contact with Europe and the Middle East grew despite the distance. It's also important to remember that most of the writings I'm mentioning (and pulling from Edward H. Schafers Iranian Merchants in Tang Dynasty Tales and Marc Abramson's Deep Eyes and High Noses) are local understandings of the outside world as opposed to an emissary or diplomat's description of the world. But indeed by the Tang Dynasty, China's understanding of the world around them at least on the continental point through the Silk Road and the Tarim Basin contained a wealth of information that carried onwards and actually informed on how diplomacy with foreigners would be conducted. This too applied to the Song, Yuan, and Ming.
On an ending note, I understand that I did not explicitly answer the question pertaining to exploration, but I'd like to point out that much of the continental exploration and contact with the world had already happened by the 1200s. Barring the large seafaring explorations of the Ming (which are an entirely different kettle of fish), I would surmise that from the Tang onwards, China (at least) showed an evergrowing interest and curiosity to the world outside of their immediate boundaries and a large degree interest in things ranging from cultural exchanges to local and regional politics despite the sheer distance of cultures. Though perhaps the local and domestic impression of foreigners depended on visual and behavioral suggestions, the stereotyping done within those works seemed to apply on an individualistic basis as leaders and important emissaries always had differing descriptions written about them. In fact there are one or two generals within the Tang who were actually praised for being "beast-like" and were Turkish as opposed to native "chinese."
There's a lot more to uncover here, like the relation to how "Chinese" identified themselves vs. foreigners, but I'll do a follow up if requested instead. :)
Sources:
Edward H. Schafer, Iranian Merchants in Tang Dynasty Tales
Marc Samuel Abramson, Deep Eyes and High Noses: Constructing Ethnicity in Tang China