The news comes as Lauer continues to be widely criticized for last year's firing of his co-anchor Ann Curry. Lauer is also being partially blamed for the loss of "Today" viewers to its ABC competitor "Good Morning America."
Deadline said NBC told Lauer it was courting Cooper as his replacement and asked Lauer to give the transition his stamp of approval.
Instead, Lauer allegedly called Cooper to voice his outrage over the prospect of being replaced before he is ready to leave.
Lauer's call surprised Cooper, who thought Lauer supported the "Today" show change, the entertainment industry news website said.