"I need to assess the squad and take it from there. Kevin and me go a long way back, as everyone knows," Allardyce said after being unveiled as Sunderland's manager on Tuesday.
"Nolan is an addition I may look at in the future, I may choose to enter down that line but at the moment it's about giving the players I've got here an opportunity to show what they can do," he added.
Nolan and Allardyce have a long history together and the manager made the midfielder his captain during their long stint at Bolton Wanderers.
Allardyce also managed Nolan briefly at Newcastle before signing the midfielder for West Ham and handing him the armband.
Nolan's success with Newcastle during his 2-1/2 years at the club has not endeared him to Sunderland's fans.
He scored a hat-trick in a north-east derby against Sunderland in 2010 and has shared a tempestuous relationship with their supporters for years.
The 33-year-old has been training with fourth-tier side Leyton Orient since leaving the Hammers.
Sunderland welcome Newcastle to the Stadium of Light in their first Premier League derby of the season on Oct. 25, after they travel to West Bromwich Albion on Saturday.
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
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