I just don't see this being a runner. Firstly, there is - however much one may deny it - a political factor; Aer Lingus is very much a symbol of national pride and while that may cut no ice in the commercial world, a government already unpopular and with two years to run before an election, is not going to want to sell Aer Lingus to BA; a vast majority of public opinion would not have it and it's certainly something that could be whipped up by opposition parties. Sinn Fein, which has been successfully attacking FF's core vote in many constituencies would have a field day.
There will be concerns about Aer Lingus being used as slot fodder for BA.
However, the real question is what BA could bring to Aer Lingus. They are clearly huge differences between them. EI is going down the low cost route; BA is going the quality route and has a far bigger business/premium class base than EI. The two airlines work together in oneworld, but I don't see what synergies can be achieved by the two of them coming together.