Moments before he had said he did not think the RFU review into England's campaign, and his own future, had begun.
"You never know!" he quipped. "But I'd like to think I'd know if it had. Of course I'll have input in it, absolutely."
The response of the RFU, who had been made aware of the story before the press conference but seemingly not alerted Lancaster, was to deny any approach.
Mallett is just the latest name to be linked to replacing Lancaster. New Zealand's Wayne Smith, Ireland's Joe Schmidt, Japan coach Eddie Jones and even Kiwi-born Wales mentor Warren Gatland are being bandied about in the international press as contenders.
Sir Graham Henry, writing in the Guardian, expressed sympathy for Lancaster's plight and his early exit from the tournament but suggested he would be a better coach for the experience and that England should retain faith in him.
"I can empathise with Stuart Lancaster because I know what he is going through," Henry said of his own experience in 2007. "It's hell, and I hate with a passion going back there, making this difficult to write.
"But, looking back, the experiences I learned most from were the quarter-final in 2007 and the Lions tour six years earlier. All long-term professional sports coaches go through difficult times. It is a rollercoaster ride and what doesn't kill you makes you stronger. Survival and having the opportunity to learn from those experiences is key.
"I was fortunate to remain as the head coach of the All Blacks and I hope Stuart enjoys the same fortune when the English union, after getting over its initial shock and hurt, reflects soberly on what happened."
The continued open speculation came as England absorbed another setback when World Cup organisers imposed restricted match access on assistant coaches Andy Farrell and Graham Rowntree for the game against Uruguay after the pair breached Cup rules by approaching the referee at halftime in last weekend's clash against Australia.