The European Commission must decide on Ryanair's bid by March 6, but a decision could be made sooner.
While Mr Mueller continues to resist the takeover bid, former Aer Lingus chief executive Willie Walsh said on Saturday that it should be allowed to go ahead.
Mr Walsh, who is chief executive of British Airways owner IAG, said the global airline industry needs to consolidate. He added that the State is against the Ryanair bid for "purely emotional, not rational" reasons. The Government has said it won't sell its 25pc stake even if Ryanair gets the green light to buy Aer Lingus. Mr Walsh added that he believes Ryanair has a better than 50-50 chance to success.
The IAG boss has agreed to offer extra routes between Ireland and the UK if the deal goes ahead. His comments, and the deal, are part of a gradual thawing of relations with Mr O'Leary. Mr Walsh said late last year about Mr O'Leary that: "I don't agree with everything he does and says, but I don't think you can take away the achievements he and Ryanair have had in terms of financial performance. He's demonstrated that you can be profitable in this industry even in a downturn."
It emerged yesterday that US Airways Group and AMR are nearing an $11bn (€8.2bn) merger that would create the world's largest airline and could announce a deal within a week, after resolving key differences on valuation and management structure.
Sources told Reuters that a deal that was still being finalised would make US Airways chief executive Doug Parker chief executive of the new airline while AMR's Tom Horton would serve as non-executive chairman.
The deal would come more than 14 months after the parent of American Airlines filed for bankruptcy in November 2011, and would mark the last combination of legacy US carriers, following the Delta-North- west and United-Continental mergers.
The merger is expected to value the combined carrier at between $10.5bn and $11bn (€7.8bn-€8.2bn). AMR creditors would own 72pc of the new company, with US Airways shareholders owning the rest.
The board of each airline is expected to meet in the middle of the coming week to vote.