Given was again outstanding in their victory over Stoke on Saturday.
Mancini may hail from the land that spawned Gianluigi Buffon, generally regarded as the world's number one, but he has no doubt Given is a class act too.
"Shay is among the top five keepers in the world," said Mancini.
"You have Buffon, (Petr) Cech and a couple of others but Shay is right up there. Against Stoke he made saves in one or two situations that were absolutely crucial."