For younger players, I would renew near the start of the season, because they will ask for more as they develop.

For older players, I would renew towards the end of the season, because they won't grow that much so you shouldn't pay them more over the season.

Think carefully about it because you might decide you do not want the player next season and then you will have wasted money on the renewal. I never renew contracts as I sell players every season, at most two seasons. As far as I know, it has no effect on performance.