The couple welcomed daughter Monroe and son Morocco in Los Angeles in April but have yet to release public images of the children.
However, Carey and Cannon are in talks with several magazines for the rights to the photos, according to the New York Post. The images are expected to fetch up to $200,000 (£125,179).
"Mariah and Nick are more concerned with doing the right thing than going to the highest bidder. They're talking to a number of publications about doing it in the best and most tasteful way," a source said.
"Nick has said on radio he doesn't feel entirely comfortable selling pictures of his children. But the first picture remains very valuable to the paparazzi."
Cannon recently revealed that Carey does not want more children while he would like to further expand their family in the future.