The comment by press secretary Sarah Sanders came in response to a tweet by ESPN host Jemele Hill, who this week launched a series of Twitter attacks on the president.
Sanders said the remarks by Hill were "outrageous" and "certainly something that I think is a fire-able offense by ESPN."
In a series of tweets this week, Hill called Trump "the most ignorant, offensive president of my lifetime," and then described him as "a white supremacist" who has surrounded himself with other white supremacists.
Hill's comments were the latest fallout from Trump's mixed messages about violence at a white supremacist rally in Charlottesville, Virginia, that resulted in the death of a counter-protester.
The remarks also appeared to escalate tensions between conservatives and the sports network which some have accused of being too political.
ESPN, a unit of the Walt Disney Co., said in a statement that Hill's comments on Twitter "do not represent the position of ESPN," adding that "we have addressed this with Jemelle and she recognises her actions were inappropriate."
