Three low-cost airlines operate from Heathrow at present: Aer Lingus, which is subject to a bid by BA's parent, IAG; Vueling, which is part of IAG; and the Lufthansa subsidiary Germanwings.
Walsh and IAG have said that Aer Lingus would also continue routes between Heathrow and Cork and Shannon for the next seven years, as well as retaining its distinct Irish corporate brand.
The chief executive of IAG, the parent of British Airways and Iberia, is close to securing control of Aer Lingus after the Irish government agreed to sell its own shareholding in the former flag carrier to the group.
However, Walsh would not name the four extra transatlantic routes IAG was reported to have planned for Aer Lingus if the takeover completed.
Craig Kreeger, chief executive of Virgin Atlantic, promised that despite the predictions of rival IAG boss Willie Walsh, Delta would not subsume Branson's airline.
IAG is offering Aer Lingus shareholders €2.55 in cash per share, under the proposed deal backed by the airliner's management but disputed by trade unions and opposition parties in Ireland.
Speaking in Dublin on Wednesday after the Irish government gave the go-ahead for the sale of its 25% stake in Aer Lingus, the IAG boss also vowed that the Irish carrier's Heathrow-to-Ireland slots were not under threat.
Walsh said on Wednesday that IAG would make a formal offer within the next 28 days for Ryanair's shareholding and he did not expect the low-cost airline to stand in the way of a deal.
"As an Irishman I'm very proud … but this is not a Willie Walsh initiative; it is an IAG one," he added.
Indeed IAG, in which Qatar owns a 10% stake, recently pulled out of a European trade association saying the group's opposition to the super-connectors, led by AF-KLM and Lufthansa, was no longer consistent with its own position.AF-KLM and Lufthansa themselves have tried to make up for years of bad management by beefing up their budget subsidiaries, Transavia and Germanwings.
IAG still needs the support of Ryanair, which holds a 30% stake in Aer Lingus, for its bid to succeed.
