Former Sun editor Kelvin Mackenzie is to leave the paper after making controversial comments in a column about Everton footballer Ross Barkley.
He was suspended after comparing the player – who is white, but has a Nigerian grandfather – to a gorilla.
The BBC’s media editor Amol Rajan said: “Now we know he will not be asked to contribute to the paper again”.
A spokesman for The Sun said Mr Mackenzie “remained suspended” but would not comment on his departure.
According to the Financial Times, the terms of Mr Mackenzie’s exit are being negotiated.
In the article, Mr MacKenzie said looking at Mr Barkley’s eyes had given him a “similar feeling when seeing a gorilla at the zoo”.
His eyes made him “certain not only are the lights not on, there is definitely nobody at home”, he wrote.
Alongside the article, was an image of a gorilla next to a picture of the midfielder.
The paper subsequently apologised for the article, published on 14 April, saying it was unaware of Mr Barkley’s heritage.
The Sun’s subsequent apology said that as soon as Mr Barkley’s background was drawn to its attention, the article was removed from its website.
The apology did not extend to other elements of the article, in which Mr MacKenzie suggested that the only people in Liverpool who could earn as much as footballers were drug dealers.
Liverpool mayor Joe Anderson had called for Mr Mackenzie to be sacked over the column, describing it as a “racial slur” and a “disgrace”.
At the time, Mr Mackenzie said he was unaware Barkley had a Nigerian-born grandfather and denied the column was “racist”.
The Sun’s publisher, News UK, is part of News Corp, run by Rupert Murdoch.
Ofcom is currently examining an £11.7bn bid from 21st Century Fox, also run by Mr Murdoch, of broadcaster Sky, of which it already owns 39%.
The BBC’s media editor said Mr Murdoch and the company hoped that by showing they were willing to sack long-standing stars they will send a signal to media regulator Ofcom that they are fit and proper to own Sky outright.