33-year-old Nolan, currently a free agent after leaving the Hammers in late August, is on the lookout for a new club and has naturally been linked with the Black Cats following Allardyce's appointment.
But the new Stadium of Light boss will have to cast more of an eye over his current crop before making such decisions.
"I have to assess the squad and whether I need another midfield player," said Allardyce.
"Kevin and me go back a long way but I need to assess the ability of the squad and then take it from there.
"If I feel Kevin may be someone I can look at in the future, and will give us something, then that may be a line I enter down."