The overseer of the net's addressing system has asked the US government to be freed from official control.
Icann made the plea in a lengthy report sent to the US Department of Commerce.
The report will be the focus of a meeting to consider Icann's progress on objectives the US government set it in preparation for independence.
Icann argues these objectives have been achieved earlier than planned and now is the time for talk to turn into deciding what happens on independence.
Paul Twomey, president of Icann, told the BBC news website that the process of meeting the objectives was "essentially complete".
The US government issued a call for comments on Icann's progress prior to the meeting.
Mr Twomey said the lengthy report was part of Icann's response to this request detailing its achievements.
The meeting marks the half-way point for the Joint Project Agreement (JPA) under which Icann was tasked to comply with a series of "responsibilities" deemed necessary for its release from official oversight.
The JPA grew out of the original Memorandum of Understanding that established Icann and signalled the beginning of the end for US control.
"The Board proposes that the JPA is no longer necessary and can be concluded," wrote Peter Dengate Thrush, chairman of the Icann board, in the letter accompanying the report.
Added Mr Twomey: "Has the process of the MoU and JPA towards building a stable, strong organisation which can do this transition, has that been successful? The board is effectively saying yes."
Instead of creating more hoops for Icann to jump through, Mr Twomey said it was time for talk to move on and for thoughts about the future of the net body. Icann keeps an eye on the net's addressing system - the master directories of which site is where.
Said Mr Twomey: "The JPA has been fundamentally achieved and what's more important is for the Department of Commerce and Icann to talk about what the next stage looks like."
But, he added, this did not mean that Icann's work was done.
"If the question is: 'Can Icann keep improving?' then, yes, of course it can but that's not the question," he said. "The time now is really to talk about what the final transition is going to look like."
In the future Mr Twomey said governments would still have a role in keeping the organisation informed about public policy developments but would not be able to dictate its agenda or development.
He said one of the principles Icann had worked towards fulfilling was freedom from official influence.
Icann is due to meet the officials from the US Department of Commerce in March. Anyone wishing to comment on its progress towards being a private body has until 14 February to let their views be known to the US government.