Free agent

The commercial position follows from the definition of transfer compensation: a fee is what a new club pays in exchange for the former club agreeing to release the player from a binding contract. Where there is no contract there is nothing to be released from.

Registration is the part people get wrong. Being a free agent does not mean being registrable at any time. The regulations set out specific circumstances in which an association may exceptionally register a player outside a window, and they are narrower than the folklore.

A professional whose contract has naturally expired, or was mutually terminated, before the end of the registration period applicable to the engaging club may be registered after that period has closed. A professional who terminated with just cause, or whose club terminated without just cause, may also be registered outside a window, with the FIFA general secretariat making a prima facie assessment of which it was on receiving the ITC request. That assessment is provisional and does not bind the Football Tribunal on the consequences.

Note the timing in the first of those. What matters is when the contract ended relative to the window, not when the player signs.