HITC Sport understands that the former West Ham manager is to cast an eye over free agents he knows well.
Allardyce knows he cannot do much work on his new squad until the transfer window opens in January, but Premier League clubs can still sign free agents and he is ready to investigate that market.
HITC Sport understands that Kevin Nolan, Carlton Cole and Ricardo Vaz Te are set to be offered the chance to train with the Black Cats in the coming weeks, with a view to earning moves to the Stadium of Light.
33-year-old Nolan left West Ham by mutual consent just before the transfer window closed last month, and he has been in talks with a number of clubs.
But now the chance to link back up with Allardyce, who he has spent much of his career with at Bolton and West Ham, does appeal, whilst it would also mean a return to the North East where he enjoyed a spell with their rivals Newcastle.
Forwards Cole and Vaz Te are also being looked at by Allardyce, as both could offer extra options in attack for the misfiring Black Cats.
If all impress and do enough, they could be handed short-term deals with a view to earning longer stays on Wearside.