Not entirely true. I have players that are 38 Q on the list, have one right now as we speak.
Any player that is 1 or 2 Q away from the next star gets placed automatically on the negotiations list for sale.
I had something similar when I was at level 4, but it seems to become less common when you go up the levels. Maybe less players are likely to be put on the negotiations list as it is a new unlock for lower levels?
Rhondda Rovers (The Rebirth) - Season 5, Level 3
Career Progress:
League Titles - 3 Cup Winners - 1 Champions League Winners - 1