The Luther actor says that when he met the rapper he was immediately reminded of the role that made him a star in the US.
'There's a way Jay-Z looks you dead in your eye and doesn't look away that reminded me of Stringer,' Elba, 39, tells Essence magazine.
The irony of the comparison is not lost on the Hackney-born actor who is aware of the rapper's past career as a drug dealer.
Born Shawn Corey Carter, Jay-Z started selling crack cocaine in his Brooklyn neighbourhood when he was just 13.
The 41-year-old has been open about his criminal past.
Elba met Jay-Z at the premiere of Obsessed, the 2009 film he starred in opposite the rapper's wife, Beyonce.