Sunderland are reportedly willing to allow Everton target Lamine Kone to be sold for a price of £10 million.
Allardyce took Kone to Sunderland two years ago and the Ivory Coast international delivered some inspirational performances during the second half of the 2015-16 season as he helped the Black Cats to avoid relegation from the Premier League.
He however struggled for consistency last season as the Black Cats were relegated from the top flight after finishing in last position on the League standings.
As Sunderland are in financial trouble, they are likely to sanction a sale of Kone in order to bring in much needed funds to the club.
The Toffees previously tried to sign Kone for £19 million during the summer of 2016 but the transfer was blocked by the Black Cats. The player afterwards admitted that he was gutted that the move did not go ahead.
He said: “Everton, they are not a small club. There were other clubs interested too. But it was not concrete like Everton.
“It was a very good opportunity for me. A golden opportunity. They are playing for the top positions. They could be in Europe.
“So it was an interesting challenge for me. At the time, I was disappointed.”