Sir Tim Berners-Lee - inventor of the world wide web - is the latest voice to raise concerns about a meeting of communication tech regulators in Dubai.
He spoke of concerns that some attendees would push for a UN agency to "run the internet" rather than leaving it to groups already "doing a good job".
Internet pioneer Vint Cerf has also highlighted the issue on Google's site.
But the UN agency itself is playing down suggestions of a power-grab.
Dr Hamadoun Toure, secretary-general of the UN's International Telecommunications Union (ITU), said ahead of the event: "There is no need for the ITU to take over the internet governance."
The United Arab Emirates is playing host to 193 countries at World Conference on International Telecommunications (Wcit).
They aim to revise a telecommunications treaty which has not been overhauled since 1988.
The ITU has said there was a need to address the fact technologies like the internet were not properly addressed by the current regulations, and that more efforts must be made to change the fact that "two-thirds of the world's population" did not have access to the net.
Among the proposals being considered is a clause put forward by Russia which says: "Member states shall have equal rights to manage the internet, including in regard to the allotment, assignment and reclamation of internet numbering, naming, addressing and identification resources and to support for the operation and development of basic internet infrastructure."
This has been interpreted by some as a starting point for domain name regulator Icann, the Internet Engineering Task Force and other organisations that oversee the internet's technical specifications to be forced to be pass at least some of their powers to another body such as the ITU.
Sir Tim is director of a standards body himself - the World Wide Web Consortium. He said that governments can already influence changes but should resist further interference.
"I think it's important that these existing structures continue to be used without any attempt to bypass them," he said.
"These organisations have been around for a number of years and I think it would be a disruptive threat to the stability of the system for people to try to set up alternative organisations to do the standards."
Sir Tim also indicated that there was no need to create new internet-specific sections to an international treaty in order to improve access.
"It seems that at the moment the growth of the internet is spectacular and the developing countries have the highest growth rate.
"A few years ago we started [World Wide] Web Foundation worrying that connectivity was relevant, but now today connectivity is clearly becoming ubiquitous - we need to look at other concerns such as net neutrality and whether governments spy on the internet and whether they block it.
"A lot of concerns I've heard from people have been that, in fact, countries that want to be able to block the internet and give people within their country a 'secure' view of what's out there would use a treaty at the ITU as a mechanism to do that, and force other countries to fall into line with the blockages that they wanted to put in place."
However, Sir Tim added that resistance to such an idea by other nations would mean the problem could be avoided.
The ITU's leader has said he intends to prevent any measure being put to a vote, and that proposals must be agreed, instead, by consensus.
The US has already made clear that it would block any attempt by Russia or another country to make changes to internet governance.
"We will actively oppose the Russian proposal," said Terry Kramer, the US ambassador to Wcit, last week.
"We have had good working relationships with our Russian colleagues, but the proposal that actually came out, to us, was shocking."
The US is now pressing for there to be no reference to the internet in the treaty.
Early discussions at Wcit have included a debate over an internet-related clause championed by Tunisia.
It said the revised treaty should contain a clause committing member states to protecting freedom of expression on the net including "the freedom of online peaceful assembly".
The ITU said the text sparked a "vigorous debate", but was deemed unnecessary since such the issue was already addressed by human rights treaties which take precedence over whatever would ultimately be included in the communications agreement,
The conference continues until 14 December.