You are correct. OP, if his renew button is greyed out so will be his sell button. So you will lose him in 8 days from now.
Unless new app is different you get no warning that a player will retire next season so its pot luck with old players.
PS players don't retire until 32 at the earliest, not 31 as stated above. So if money is an issue for you it is advisable to sell any 31 year olds you have unless they are true match winners. (By which i mean Regular 8+ ratings,3-4 MVP this season)