At an event in Hove, the prime minister said all good schools should be able to expand and his government had supported that right.
The Weald of Kent girls' grammar school wants to open an annexe in Sevenoaks.
The Department for Education (DfE) is considering the plans which have the backing of Kent County Council.
The law forbids the opening of new grammar schools, but changes made by the coalition government in 2012 allow enlargement of existing schools.
"I strongly support the right of all good schools to expand. I think that's very important and that should include grammar schools," the prime minister said:
"Under this government grammar schools have been able to expand and that is all to the good."
Mr Cameron was responding to a question about the the proposed satellite grammar school in Sevenoaks.
But he would not be drawn on when the government was likely to make its decision.
"As for the decision that the Department for Education has to take, they have to take that having [looked] at all the evidence and after having proper consultations and making the decision in proper time," he added.
Sevenoaks is the only major Kent town that does not have grammar provision.
Bids made in 2013 were turned down because the DfE said they did not comply with the law.
But the current plans put forward by Weald of Kent girls' grammar school are believed to have met the criteria.
If approved, the annexe could pave the way for more grammars to open satellite campuses.
General secretary of the National Union of Teachers, Christine Blower, has previously called the plans for grammar school expansion "yet another unnecessary distraction".
David Cameron has voiced his "strong support" for the expansion of grammar schools during a visit to the South East.