Meopham School - for boys and girls - has outlined plans to consult parents on converting to a mixed-sex grammar by 2018.
Pupils would gain entry by sitting the Meopham selection test, The Swale Academies Trust has said.
The trust has stressed the consultation plans are in their earliest stages.
Theresa May's plans for more grammar schools in England have been given a lukewarm welcome by the former Chancellor, George Osborne.
Education reforms whilst he was in government focused on the comprehensive system as a whole - in particular creating new academies and free schools.
He said he welcomed some selection in schools, but said it was wrong for politicians to focus on the brightest children.
Meopham principal Jon Whitcombe said in a letter to parents, the trust believes there is a need for additional grammar school places in the area.
"We also believe many parents would welcome the opportunity to have a local mixed grammar school provision as an alternative to the current single sex grammar schools," he said.
Pupils already at the school would not be affected, but those wishing to join from 2018 would need to take a selection test.
"Swale Academies Trust recognises that this is a potentially contentious issue," said Mr Whitcombe.
"However, it is important to stress that this proposal is at the very earliest stages of development and that we are actively interested in ensuring a thorough and balanced discussion over what is right for the school and the community prior to any decision being taken."
A non-selective school in Kent is believed to be the first to outline plans to become a grammar school after Theresa May outlined education changes.