The City of London Academy in Lynton Road is proposing to create a multi-academy trust with Redriff Primary School, with the City of London Corporation extending its sponsorship to include the Rotherhithe primary school.
The Salter Road school is one of main feeder schools for the City of London Academy and the schools hope that by easing the transition from primary to secondary schools they can boost pupils' achievement.
CoLA, which opened in 2005 on its Lynton Road site, is one of three London academies sponsored by the City of London Corporation.
William Fraser, chair of governors at CoLA, and Lucas Green, chair of governors at Redriff, have written to parents of pupils at both schools setting out the proposal for closer cooperation between the two institutions.
"We want to ensure the individual identity and independence of each school is preserved and so the governors are proposing the setting up of a multi academy trust including both academies and that the City of London become a sponsor of Redriff Primary Academy," say the chairmen in their letter.
The letter continues: "Overall parents would not notice a difference in the day to day school life. Federating the academies through the multi academy trust, could, however, make a significant difference on how we build on the current successes and ultimately how well pupils and studentsí progress."
The two academies would be operated by a single charitable company with a single board of directors, though some functions would be delegated to individual governing bodies.
A consultation period on the proposal continues until 18 June; details at www.cityacademy.co.uk