Does the WTO monitor the trade of players in association football? Could they? So I understand the WTO is able to settle trade disputes. If the German Bundesliga said English players had a 1% luxury fee that went towards operation costs (A \$100,000 transfer would cost \$101,000, with \$1,000 going to the Bundesliga), would the WTO be able to step in if England went to them? What if the German government were to impose a 1% tax instead? If these aren't under the purview of the WTO, could they be in a decade?
No, for several reasons.

WTO deals with trade disputes between nations when one nation creates legislature that breaks WTO rules or some pre-existing trade agreement. For example, one of the most important WTO rules is the most favored nation principle which says that (WTO, 2020):


countries cannot normally discriminate between their trading partners. Grant someone a special favour (such as a lower customs duty rate for one of their products) and you have to do the same for all other WTO members.

But again this all applies to countries not companies. Companies can charge different prices to people in different countries if they want to.

Trading players would likely not even qualify as a trade. If one company releases player from a contract and that player then signs contract with another company that is no more trade in economic terms than when your company fires you and other company in another country hires you. For this to qualify as a trade the players would still have to be employees of the UK company and just provide service to the German company  (when this would become trade in services).

Even if there would be trade in services and $1\%$ government imposed tax this would not be violation of WTO rules as long as all countries Germany trades with are subject to this $1\%$ tax or if it would be part of some of the WTO exceptions (for example, WTO allows trading blocks to set among themselves lower barriers than just under pure most favored nation principle).



If these aren't under the purview of the WTO, could they be in a decade?

I doubt this would ever be under the purview of the WTO given that WTO's objective is to promote free trade by removing tariffs and non-tariff barriers to trade and trade cooperation amongst nations. WTO's objective is not to regulate/police trade among private firms. In addition depending on how the 'trading of players' is set up it does not even qualifies as a trade (e.g. if players change employer).