The Sun's parent company is in negotiations with its former editor Kelvin MacKenzie over the terms of his departure, according to reports.
News UK is believed to have decided to part company with the columnist after he wrote a piece comparing Everton and England footballer Ross Barkley to a gorilla, according to the Financial Times.
The Sun published a story headlined Ross Barkley: Sun Apology, after the April 14 opinion piece in the paper sparked outrage, and MacKenzie was suspended.
Alongside the column, which made disparaging remarks about the star, was a photograph of a gorilla's eyes below a close-up of the eyes of Barkley, whose grandfather was born in Nigeria.
The Financial Times reports MacKenzie will not be employed by News UK for "much longer".
It is thought terms of his departure could be agreed within the next week.
A spokesman for The Sun said: "Kelvin remains suspended from the newspaper."
However he refused to comment on whether the tabloid was in exit negotiations with its former editor.
Speaking to the Press Association after his suspension, MacKenzie said: "I had no idea of Ross Barkley's family background and nor did anybody else.
"For the mayor of Liverpool and a handful of others to describe the article as racist is beyond parody."
In his column, MacKenzie had written: "Perhaps unfairly, I have always judged Ross Barkley as one of our dimmest footballers.
"There is something about the lack of reflection in his eyes which makes me certain not only are the lights not on, there is definitely nobody at home.
"I get a similar feeling when seeing a gorilla at the zoo. The physique is magnificent but it's the eyes that tell the story."
MacKenzie's suspension was announced on the eve of the 28th anniversary of the Hillsborough disaster in which 96 Liverpool fans died.
He was editor of The Sun when it published a front-page article headlined Hillsborough: The Truth in the aftermath of the 1989 disaster at Sheffield Wednesday's football stadium.
The article claimed Liverpool fans were to blame for the tragedy. MacKenzie apologised in 2012.