As already stated, Law 4 of the "Laws of the Game" states that shorts are compulsory.
However, FIFA's supplemental document "Equipment Regulations" elaborates on Law 4 stating:
3.1 ... the basic compulsory Equipment of a Player
comprises the following separate Equipment items:
b) shorts (for goalkeeper, shorts or tracksuit trousers);
In addition to this, there are a myriad different rules and guidelines for shorts, relating to numbering, manufacturer's logo and team badge but nothing specifying the length of the shorts.
To that end: Shorts below the knee are permitted.
However, I doubt we'll be seeing them any time soon because, from personal experience, the extra fabric inhibits the movement of the knee joint. This makes longer shorts impractical, which is likely why FIFA doesn't need to mention them.