Today, what I can only see is my club history in terms of trophies or positions.
Since this information is accessible to me, the same information could be accessible to any (league/cup/champions league/super league) opponent I face or friend I have in the game.
Such information is already stored in a server and it will be retrieved/cached upon respective request from every user that complies with the above criteria.
Further on, more club statistics could be available on per user team basis and perhaps only to the authenticated user (namely, not accessible by other players), in terms of:
a) number of wins/defeats/draws per competition (home/away/total) per season/total (excl. associations)
b) total Goals For & Goals Against
c) biggest win/loss difference
d) more goals scored/suffered in a game
e) top goalscorer/assist/GK/defender
f) etc. ...
Limitations shall always exist, but this will be less of an issue over time (due to communications ecosystem advancement).