Chinese admirals are pushing their government to help them establish a support base near the Persian Gulf. The immediate need is for an easier way to supply the Chinese warships working with the anti-piracy patrol off Somalia. This could be done by negotiating basing rights, where some Chinese naval personnel would set up shop at a port in the area, and make arrangements for resupplying and repairing any Chinese warships operating in the area, as well as allowing the Chinese warships to tie up in the local port for extended periods of time. Such arrangements are basically a commercial undertaking, but must be negotiated government-to-government because military forces are involved. Many nations have such arrangements in the region, particularly the Persian Gulf. Chinese sailors coming ashore would basically be treated like tourists, and subject to local law. This can get sticky if sailors misbehave, as sailors sometimes do, and get arrested. Many sailors on Chinese warships have access to classified information, and no navy likes having their sailors under the control of a foreign government. It's feared that the police investigation will include agents from a local, or foreign, intelligence, agency.
Thus there is a tendency for the basing rights to evolve into a naval base, complete with a "status of forces" agreement which allows the Chinese navy to discipline misbehaving sailors, in cooperation with local authorities (so the sailors don't get away with anything, especially in the eyes of the locals.) Allowing a foreign navy to establish themselves on your territory is a touchy subject, and must be handled carefully. The Chinese would be expected to be generous and useful guests. But, at the same time, the full time presence of the Chinese navy would mean a military relationship with the local host, and a willingness to help the host out in the event of any diplomatic trouble or military threat. This works both ways, as a major rationale for a Chinese naval base in the region is to protect the growing traffic in sea traffic of raw materials headed for China, and manufactured goods coming in from China. Everyone has an interest in insuring that this sea traffic moves unhindered by pirates, or any other manmade threat. Well, almost everyone.
India is not enthusiastic about a Chinese naval base in the region. India sees China as a military, diplomatic and economic competitor. India sees itself as the master of the Indian Ocean, and China as an unwelcome interloper. Thus any Chinese effort to establish a naval base in the Western Indian Ocean would be opposed by India, and many existing Indian allies in the area.