"This is very helpful," the Democratic front-runner joked. "Don't tell anyone because we want it to be a big surprise."
"Now you have to choose and, obviously, it's me," DeGeneres said in clips that the show released in advance.
"I already offered it to you," Clinton said. "...You turned it down."
Earlier in her appearance on the show, which was taped Tuesday, Clinton was asked about Trump and his comments that he would be good for women.
"I would need a lot more information based on what I hear him say because he has been very derogatory towards all kind of women," Clinton argued, adding, "I think, overall, there is just no evidence that he has an understanding of what women’s lives are like today."
When asked whether Sanders should drop out, Clinton answered, "he has to do what he chooses to do. I understand that."
The full interview is set to air today at 4 p.m. ET.