In a statement to the Irish Stock Exchange, the airline says the offer values Aer Lingus at approximately €694 million.
Ryanair already owns 29.82% of Aer Lingus, a stake acquired over five years ago.
The stake was reviewed by the European Union and has recently been referred by the UK Office of Fair Trade to the UK Competition Commission.
Ryanair will make the offer through a wholly owned subsidiary Coinside Ltd.
The 29.8% stake was acquired for the most part by Ryanair between late 2006 and early 2007.