The Invincible Class ships - Illustrious, Invincible, and Ark Royal - were introduced in the 1980s.
The Invincible was recycled and the Ark Royal is due to be sold as scrap metal.
However, the Ministry of Defence (MoD) said Illustrious, based at Portsmouth in Hampshire, would be preserved after it left service in 2014.
It is now seeking proposals from organisations with ideas on how best to maintain the ship.
Philip Dunne, a defence minister, said: "It is important that we preserve the legacy of the Royal Navy's Invincible Class aircraft carriers.
"When the last of these - HMS Illustrious - retires from the Royal Navy, we would like to see her preserved as a legacy to the work she, Invincible and Ark Royal have done to protect the UK over three decades.
"We would be keen to seek innovative proposals from a range of organisations, including private sector companies, charities and trusts."
The Invincible Class ships have played key roles in conflicts including the Falkland Islands, Iraq and Bosnia.
The MoD said "new, much larger" Queen Elizabeth aircraft carriers would start to enter service in 2017.
The aircraft carrier HMS Illustrious will be preserved as a lasting tribute to a decommission class of Royal Navy aircraft carriers.