Chelsea already have a suspended three points penalty hanging over them following their illegal approach for Arsenal left-back Ashley Cole.
Bates believes Leeds can prove Chelsea acted improperly in signing teenagers Michael Woods and Tom Taiwo from the Leeds Academy.
Bates said: "We're asking for £24m for the players. They made an illegal approach for three of our kids so, at the moment, we're going to report them to FIFA as well.
"They're sitting on the three-point deduction for Cole. So three points for each player would represent a 12-point deduction for next season."
Chelsea spokesman Simon Greenberg said: "We've always denied that an illegal approach was made for Woods, Taiwo and Rose.
"We made an approach to Leeds at the end of last year which they rejected. There was then a window of opportunity where any club could come in and make offers. Two of the players decided to join Chelsea.
"If there is an official complaint there is a process in place which can deal with this kind of matter."
Chelsea failed to persuade Danny Rose to join the exodus south.