The Scottish bank had agreed to meet senior Barclays executives to discuss a possible merger back in February, only for the meeting to be cancelled at the last minute after Mr O'Neill had agreed to join the group.
The RBS chief executive, Sir George Mathewson, is now understood to be planning fresh overtures in the light of yesterday's developments.
The prospect of a bank mega-merger helped drive the FTSE 100 up more than 70 points to a record high of 6,513.1.
RBS and Barclays - which have both risen by 40 per cent so far this year - rose sharply again yesterday, putting on 62p to pounds 14.25 and 46p to pounds 19.99 respectively as merger speculation took hold.
RBS is believed to have identified potential cost savings of pounds 200m from a merger with Barclays, in addition to the benefits it would bring to the bank by providing an instant solution to its leadership crisis. The bank has a tried and respected senior management team headed by Sir George and Fred Goodwin, the deputy chief executive who joined RBS last year from National Australia Bank.
One investment banker said yesterday: "Mathewson and Fred Goodwin, his deputy, are an impressive team."
Because of the disparity in size, the deal would have to be structured as a reverse takeover by RBS of Barclays, with Edinburgh being given at least a symbolic role as group headquarters in order to pacify Scottish public opinion in the run up to the first Scottish assembly elections. RBS has a market capitalisation of pounds 12bn against pounds 20bn for Barclays.
Sir Peter Middleton, Barclays' acting chief executive, insisted yesterday that the bank would not be panicked into a merger, but neither would it reject reasonable propositions out of hand.
"We've demonstrated that we can push the business forward with the divisional heads," he said.
The bank was confident that having done much of the spadework already, the headhunters Spencer Stuart would be able to come up with alternative candidates within a reasonable timeframe.
However, investment bankers warned that given the current merger frenzy in Europe and the growing likelihood of Britain joining the euro zone before long, institutional investors bitten by the merger bug may not have the patience to sit tight and wait for the search for a new chief executive to bear fruit.
One financier said last night: "They have seen what has happened to bank share prices abroad where mergers have taken place. We have been waiting over a year for a merger in the UK banking sector and nothing has happened. Earnings are steady but not spectacular, business is flat; the market is looking for something else to take the FTSE on. This might be the gap everyone has been looking for."
Outlook, page 17