The centre-half was at Liverpool for eight years, and two years ago joined Danish club Brondby.
He is a free agent this summer, and could be tempted back to England to reunite with Benitez, who was at Liverpool between 2004 and 2010.
Benitez is yet to agree to stay on Tyneside but talks have reportedly gone well with club bosses, with the Spaniard wanting total control of transfers.
Agger is 32 later this year but would add extra strength in defence as they attempt to limit their stay in the Championship to just one season.
Benitez signed Agger for Liverpool in 2006 from Brondby for £6m.