Nick Wells, chief executive of TNT Mail UK, said the service, which has already had trials in Liverpool, Manchester and Glasgow, would be a "massive challenge".
Speaking to The Guardian, he said: "If anyone can do it, TNT can. There are going to be operational challenges, we would be ridiculously naive to think otherwise.
"It's a massive challenge on a huge scale but the reality is we have the customers, appetite and resources."
It is unclear whether the rival to Royal Mail's 'final mile' service would get the go-ahead from Government ministers and comes as Royal Mail announced that it intends to hire around 30,000 temporary staff to help clear the mail backlog in the run-up to Christmas.
Commenting on the move for temporary workers, Royal Mail chief executive Adam Crozier, said: "We are absolutely determined to do everything we can to minimise delays to customers’ mail, especially in the run-up to Christmas."
TNT lobbying government to carry out door-to-door deliveries
TNT is lobbying ministers to allow the private mail operator to carry out door-to-door deliveries.