Morgan was one of 10 players set to be out of contract at the King Power Stadium at the end of the season but the Foxes have activated the option to prolong the 29-year-old's stay at the East Midlands club until June 2015.
A statement on Leicester's official website said: "The club can confirm that an option has been activated in the contract of captain Wes Morgan.
"The club has also opened discussions with the player's representatives to extend his stay beyond this date. Negotiations on a new contract are on-going."
Morgan has made 97 appearances for Leicester since joining the club from Nottingham Forest in January 2012, including 27 this season to help the Foxes top the Sky Bet Championship.
Kasper Schmeichel, David Nugent, Lloyd Dyer, Sean St Ledger, Marcin Wasilewski, Paul Konchesky, Zak Whitbread, Martyn Waghorn and Gary Taylor-Fletcher, along with manager Nigel Pearson, are set to see their contracts expire in the summer.
However, Pearson recently said the "progress has been made in certain areas regarding that issue and players' representatives are in discussions with the club".
- Sports & Recreation
- Wes Morgan