I repeat, you player will be listed in negotiation automatically, if the player meet the requirement. He will be listed without your approval so even a 9* legend may be listed as 5* for a player four levels above you. Time-up offers are ignored automatically so there is nothing to worry about.

For example, to be listed as a player with 24 quality, that player must have total stats from 3 trees of 74.8 and not anything else. If you add one more point, the player will become 25 quality gaining a star, and no longer be listed.

There are exceptions, though.