For further information, market prices of players are higher before season end. So you can sell players in auction market with higher starting price before season end. However, there are less buyers in auction market near season end. There are likely less bids on your players. Thus the final selling price may not be high. But you should also understand that there are more players available in market in season beginning. Many of them are norgen or normal young players. Buyers usually will target on these players instead of old players. So probably it is wise to try to sell old players before season end.
I usually sell players in new seasons because the selling price is usually higher, success rate is higher and I unlikely need to repeatedly place my players to auction market. However, if a unused players' contract will expire at season, I may try to sell him near season end (in case I have patience and time to do so). Then I need not to re-sign him in new season and pay him contract re-signing fee before putting him in auction market.