Yes, like Manon said, there's many trainees for sale right after the draft, and when supply is high, prices are lower. Right at the start demand will also be high, so the lowest prices you will get a week or maybe 2 after the draft, but you should be looking right away if you can find a nice trainee which isn't in a bidding war.
If you want to spend more money on a good trainee, remember to save some money at the end of the season.