The Italian was annoyed at Redknapp's comments that suggested that the Eastlands outfit had bought their way to the top.
Mancini said that any jealousy Redknapp had should be reserved for his wife, an Italian tradition.
"Harry can borrow money from us. But he should be jealous for his wife, not for Manchester City," said the 47-year-old.
"He is jealous for his wife, I hope, not for us that we are spending."
City welcome Spurs to Manchester for a crunch game on Sunday afternoon.