The Irish Government is planning an asset sale to help with the ongoing deficit. Most semi-state companies are basket cases that no buyer would touch. There are a few exceptions - ESB, Bord Gáis - but not all that many.
Seeing that the Aer Lingus shareholding is one that has a tangible value, it would probably be among the early assets to be sold.
I would imagine they would prefer a trade buyer than trying to float all those shares at the moment.