Diafra Sakho celebrates after scoring for West Ham
Senegal international Sakho, 26, was signed by West Ham under Allardyce's stewardship in the summer of 2014, having starred in France with Metz.
Few expected him to make a huge impact in England, but with 12 goals to his name in all competitions last season, he became a fan favourite and key player under Allardyce.
However, under Allardyce's replacement Slaven Bilic, Sakho wasn't quite as important to the West Ham side, and only scored five goals in 20 Premier League appearances.
Now, West Ham are looking for a new striker this summer to score goals on a regular basis, and the Daily Mail report that Sakho has subsequently asked to leave the club.
It's claimed that Sakho has spoke to manager Bilic about his future, and told the Croatian that he sees his future away from East London - which could be music to the ears of former boss Allardyce.
The report adds that Allardyce - who made a £10m bid for Sakho last month - has now improved his offer to £12m, and wants to get the deal done quickly.
With first-team football and a reunion with Allardyce on offer at Sunderland, Sakho may well fancy a move to the Stadium of Light, whilst the funds would be of great use to Bilic and West Ham in their search for a top class centre forward.
Would you accept Sunderland's £12m bid for Sakho?