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".

Olly Martins said the force, which has to save Â£7.5m over the next two years, spends Â£3m a year on its buildings.
But changes in policing technology meant officers could now share facilities, he added.
The Police Federation said it would be concerned that officers in shops may look "unprofessional".
Mr Martins said many of the county's police buildings were in need of refurbishment and no longer in the best position to serve the public, while others were under used.
An online public survey opens on Friday to asses residents' views. The survey answers will help gauge support for replacing some stations with more accessible facilities in public areas such as public buildings and supermarkets.
The PCC said operational policing was already running at maximum efficiency, so he must look to other areas.
Changes to modern policing due to the use of technology, meant "innovative ways of increasing access to the police while reducing overheads" could be considered, he added.
"In the future officers will be able to carry out much of their communications and administrative tasks while on the move, which reduces the demand on premises and increases their visibility," he said.
He said no decisions had been taken yet but "tough choices" needed to be made.
Ray Reed from Bedfordshire Police Federation, said he was not resistant to change, but "had concerns" over response times and perception.
"People already complain about response times and if you close down stations it will make things worse," he said.
"Plus I would be worried about how police would be perceived in supermarkets, it may look unprofessional.
"And [in public buildings] there is a risk element as you may get someone becoming aggressive in full view of the public.
"[Police carry out] sensitive functions in the community and we have to think how and where we place them."

The baby was found alone and abandoned at about 15:30 local time on Friday on Steelstown Road.
Police said the child was tended to at the scene by their officers and medical staff. She was taken to Tallaght Hospital.
Her condition is described as stable.
Police said they were concerned for the welfare of the child's mother and were appealing for her to seek immediate medical treatment and contact them.
David Cameron has voiced his "strong support" for the expansion of grammar schools during a visit to the South East.
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