Since then, Sunderland have struggled to repeat those feats, with most of their time in England's top-flight spent fighting against relegation, but Allardyce is hopeful of guiding them back up the table.
"Reidy's track record here is one I want to try to emulate," Allardyce said. "Reidy was the one who started this process. He started the new stadium and the new training ground. He has a legacy here, and hopefully I can live up to his standards. If I can do that we will all have great success together."
There have been suggestions that Reid could be named as Allardyce's assistant manager, in the Sunderland Echo this week, as the 60-year-old boss looks to assemble his backroom staff at the Stadium of Light.
Allardyce takes over at Sunderland at a low point, as they are currently sit five points adrift of safety still looking for their first Premier League win of the season.
Sunderland's first game under Allardyce's stewardship comes at the weekend against West Bromwich Albion.