The 61-year-old enjoyed a relatively successful four-year stint in charge of the Irons, establishing them as a Premier League force once more after earning promotion in 2012.
He left the club last summer after failing to secure a contract extension following a turbulent final season, in which a section of Hammers' fans openly criticised the manager over a perceived dull style of football.
Allardyce was unapologetic over his philosophy and hit back at those supporters in a row which continued for much of the campaign.
Consequently, the former Bolton Wanderers boss could well hear the same boos again this weekend, but Bilic, who replaced Allardyce, hopes that his predecessor is respected.
"They should appreciate that he did great for West Ham, first and foremost," Bilic told reporters in a press conference, via ESPN. "He took over West Ham in a moment when they were in the Championship and got them back straight away. He stabilised them in the Premier League and did an amazing job.
"The fans, and everyone connected with the club, should appreciate him. I don't know what the fans think of him, but you can't change the facts and the facts are in his favour, big time!"
Allardyce himself, however, has no problem with being booed, insisting that West Ham fans have a right to express their opinion about him.
Aside from subplot, Allardyce's troops could do with three points. The Black Cats sit 19th in the Premier League table, one point behind 17th-placed Norwich City.