Djibouti is already home to Camp Lemonnier, the military headquarters used by US Special Forces for covert, anti-terror and other operations in Yemen and in Africa. France, the former colonial master, and Japan also have bases in the port, which is used by many foreign navies to fight piracy in neighbouring Somalia.
Djibouti’s president said China, a major trading partner for both Djibouti and its landlocked neighbour Ethiopia, is welcome.
"France's presence is old, and the Americans found that the position of Djibouti could help in the fight against terrorism in the region," Guelleh told AFP. "The Japanese want to protect themselves from piracy, and now the Chinese also want to protect their interests, and they are welcome."
China refused to confirm or deny on Monday that it was establishing a military base in the Horn of Africa.
"Maintenance of peace and stability in the region is in line with the interests of related countries," foreign ministry spokeswoman Hua Chunying told reporters. "It's also the common aspiration of Djibouti, China and other countries in the world."
China signed a security and defence agreement with Djibouti in February 2014. But a Chinese military base in Djibouti, the first in Africa, "would definitely be historic", according to David Shinn, a former US ambassador to Ethiopia.
The US was reportedly angry about the conclusion last year of the China-Djibouti defence deal last year. But Shinn predicts that the US will take it in its stride.
"They might be a little concerned about what this (expansion well beyond the western Indian Ocean) means for the future," he said in an interview from Washington. "But as far as a base in Djibouti, particularly a modest base, is concerned, I’d be surprised if there was great unhappiness about it."
China is reportedly considering a permanent military base in Obock, Djibouti’s northern port city.
"China clearly has a goal of building a blue-water navy, which means it will at some point go well beyond the east coast of Africa and the western Indian Ocean, and it has to think — long term — about how it would be able to service its naval vessels as they go further and further, " he explained.
Camp Lemonnier, home to 4,000 American citizens, is in the south-east of Djibouti. The US earlier this month signed a 20-year lease, indicating its willingness to stay. Terms of the lease were not disclosed.
A new Chinese deep-sea port in Djibouti would be a new " pearl" in China’s "string of pearls strategy", according to analyst and writer Robert Mason, author of The International Politics of the Arab Spring.
It could provide a boost to China’s sphere of influence, which already extends from the South China Sea, along the west coast of Myanmar to the Arabian-Sea coastal port of Gwadar, Pakistan — a major destination in the China-Pakistan Economic Corridor.
"Establishing these deep-sea ports is really about securing its economic interests, projecting influence and securing oil exports from the Gulf region," Mason explained in a phone interview from Cairo.
"It's perfectly rational for the Chinese to establish that type of instrastructure, not only for anti-piracy but also because it's a key maritime route," said Africa political military analyst Lesley Anne Warner. "I don't want to use the word alarming, but what's happening is a departure from China's role in Africa, which has until now been primarily economically focussed."
Its business interests are important in both Djibouti and neighbouring Ethiopia. Trade between Africa and China, in excess of 200 billion dollars (180 billion euros), is above the continent’s trade with the European Union or the US.
In Djibouti, China is already financing major infrastructure projects estimated to total more than 9 billion dollars (8 billion euros), including improved ports, airports and railway lines.
"Money talks, especially in small and underdeveloped states run by authoritarian governments such as Djibouti — and soon Beijing, not Washington, may have the strongest voice," wrote Hudson Institute senior fellow John Lee in the current issue of Foreign Affairs.
There was speculation that Russia also wanted to establish a presence in Djibouti, but the presence of Russian warships may have created even more controversy in western nations because of the crisis in the Ukraine.
You can follow Michel Arseneault on Twitter @miko75011