The negotiations between Allen and Morgan happened on the micro blogging website Twitter.
Morgan was trying to persuade the `Smile` hitmaker to be a guest on his ITV chat show `Life Stories` but Allen put down her demand.
The `Fear` singer asked the talk show host how much he would pay to have her on his show to which Morgan responded, "Do you mean how much do you have to pay me for this career-enhancing interview?"
Allen clarified that she could only justify coming on his show by giving money to a charity that "helps women to overcome the kind of grief that I have had to experience".
The host who is set to make his US debut on the CNN show `Piers Morgan Tonight` then suggested he could offer her a fee of a million Chilean pesos, USD 2500.
But the singer, who got engaged to boyfriend Sam Cooper on Christmas day, stood her ground and said he would have to offer a million pounds to SANDS, the stillbirth and neonatal death charity, for her to appear on his show.
"Those are my terms. I`ve got no interest in coming on your show, you`ve been asking me for years," said Allen.
The Twitter conversation coincided with the lead up to Piers` CNN show, which will air in US on Monday night.
The first guest on Piers Morgan Tonight, which succeeds Larry King`s popular show, will be Oprah Winfrey.