"Arco has been playing poker without knowing there is a mirror behind them," he quipp- ed after Arco had poured scorn on Aran's defence document, which was posted on Friday.
This revealed Aran's share of estimated reserves in the BP-operated Schiehallion field west of Shetland, where it has a 17.5 per cent stake in one of the five blocks, amounted to 22.2 million barrels. Arco reacted by saying that Aran's estimate of the proven and probable reserves was "less than we had hoped", adding that oil analysts at Wood Mackenzie reckoned the reserves were worth 26.5 million barrels.
Arco's offer values Aran at just over 61p per share, compared with Friday's closing price of 68p.
But Mr Whelan noted Arco's "seamless movement in two weeks" from talking about the mere possibility of discovering oil in Schiehallion to now being "disheartened" with Aran's own estimate.
He said: "We and our partners in Schiehallion are the only ones who have a real handle on the shape of the field. Schiehallion is the most exciting oil province in north-west Europe."
Arco hit back by saying it had only ever gone on independent estimates for the Schiehallion field based on publicly available information.
Valuing the potential worth of Schiehallion, which is widely seen as the jewel in Aran's crown, is central to the bid's outcome. City calculations suggest that Aran's producing assets alone, such as the Alba and Gryphon fields in the North Sea, are worth between 30p and 40p a share.
Whether Mr Whelan really has an ace in the hole should become clear in the next few weeks. In the meantime, he is keeping his cards close to his chest by refusing to reveal how much the Schiehallion field is worth to Aran on a per-share basis.
In the absence of such information, it remains to be seen whether Arco blinks first by raising its offer.