Dibble insists the Republic of Ireland international is one of the best keepers in the world but he has also predicted a bright future for Hart, 23.
The Welshman found himself in a similar situation to Given when he was edged out of City's first team by Tony Coton more than 20 years ago.
The 45-year-old, who is the goalkeeping coach at League Two Rotherham, told the Manchester Evening News: "Shay was unfortunate in that he damaged his shoulder at the end of last season and Joe has come back from his loan spell at Birmingham and taken his place.
"But it's great for City that they've got two international keepers fighting it out - and you can guarantee that Shay will keep Joe on his toes. Shay is one of the best keepers about. He's proved that over more than a decade with Newcastle and City.
"But Joe is an up-and-coming keeper who has got what it takes to be an England regular for years to come. I certainly wouldn't want to be in Roberto Mancini's shoes having to make the decision as to which one plays."