Leicester were the opponents when City last won the FA Cup in 1969. The two sides last met in the competition in 1996 when City won a Maine Road replay 5-0.
The tie will be played on the weekend of 3rd/4th January.
Kevin Keegan told the official club site: "We have a score to settle with Leicester. We lost 3-0 just a few weeks ago at the City of Manchester Stadium.
"This is the Cup and of course anything can happen. It is our last chance to win something this season and unlike the Carling Cup it is a home draw.
"Now we have to make sure we don't leave ourselves embarrassed like we did last time against them because fair dos to Leicester they came and worked hard and won.
"Now it is another match, another day and hopefully it will be another score to the last meeting a couple of weeks ago."