U.S. District Judge Edmond Chang last week threw out the city ordinance banning retail firearms stores.
The Chicago Tribune said the city was expected to ask Chang for a delay after Mayor Rahm Emanuel said he would not appeal the ruling.
Emanuel has not provided much detail about what the proposed regulations would look like, other than that gun stores should "obviously be away from schools and areas like that."
The Tribune said the city has suffered setbacks in a series of court decisions in recent years as it attempts to reverse rulings in favor of gun advocates.
The U.S. Supreme Court struck down the city's ban on handguns in 2010, citing the Second Amendment to the U.S. Constitution.